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<div class="title">BFloat16.h</div>  </div>
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<div class="contents">
<div class="fragment"><div class="line"><a name="l00001"></a><span class="lineno">    1</span>&#160;<span class="comment">/* Copyright 2017 The TensorFlow Authors. All Rights Reserved.</span></div>
<div class="line"><a name="l00002"></a><span class="lineno">    2</span>&#160;<span class="comment"></span> </div>
<div class="line"><a name="l00003"></a><span class="lineno">    3</span>&#160;<span class="comment">Licensed under the Apache License, Version 2.0 (the &quot;License&quot;);</span></div>
<div class="line"><a name="l00004"></a><span class="lineno">    4</span>&#160;<span class="comment">you may not use this file except in compliance with the License.</span></div>
<div class="line"><a name="l00005"></a><span class="lineno">    5</span>&#160;<span class="comment">You may obtain a copy of the License at</span></div>
<div class="line"><a name="l00006"></a><span class="lineno">    6</span>&#160;<span class="comment"></span> </div>
<div class="line"><a name="l00007"></a><span class="lineno">    7</span>&#160;<span class="comment">    http://www.apache.org/licenses/LICENSE-2.0</span></div>
<div class="line"><a name="l00008"></a><span class="lineno">    8</span>&#160;<span class="comment"></span> </div>
<div class="line"><a name="l00009"></a><span class="lineno">    9</span>&#160;<span class="comment">Unless required by applicable law or agreed to in writing, software</span></div>
<div class="line"><a name="l00010"></a><span class="lineno">   10</span>&#160;<span class="comment">distributed under the License is distributed on an &quot;AS IS&quot; BASIS,</span></div>
<div class="line"><a name="l00011"></a><span class="lineno">   11</span>&#160;<span class="comment">WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.</span></div>
<div class="line"><a name="l00012"></a><span class="lineno">   12</span>&#160;<span class="comment">See the License for the specific language governing permissions and</span></div>
<div class="line"><a name="l00013"></a><span class="lineno">   13</span>&#160;<span class="comment">limitations under the License.</span></div>
<div class="line"><a name="l00014"></a><span class="lineno">   14</span>&#160;<span class="comment">==============================================================================*/</span></div>
<div class="line"><a name="l00015"></a><span class="lineno">   15</span>&#160; </div>
<div class="line"><a name="l00016"></a><span class="lineno">   16</span>&#160;<span class="preprocessor">#ifndef EIGEN_BFLOAT16_H</span></div>
<div class="line"><a name="l00017"></a><span class="lineno">   17</span>&#160;<span class="preprocessor">#define EIGEN_BFLOAT16_H</span></div>
<div class="line"><a name="l00018"></a><span class="lineno">   18</span>&#160; </div>
<div class="line"><a name="l00019"></a><span class="lineno">   19</span>&#160;<span class="preprocessor">#include &quot;../../InternalHeaderCheck.h&quot;</span></div>
<div class="line"><a name="l00020"></a><span class="lineno">   20</span>&#160; </div>
<div class="line"><a name="l00021"></a><span class="lineno">   21</span>&#160;<span class="preprocessor">#if defined(EIGEN_HAS_HIP_BF16)</span></div>
<div class="line"><a name="l00022"></a><span class="lineno">   22</span>&#160;<span class="comment">// When compiling with GPU support, the &quot;hip_bfloat16&quot; base class as well as</span></div>
<div class="line"><a name="l00023"></a><span class="lineno">   23</span>&#160;<span class="comment">// some other routines are defined in the GPU compiler header files</span></div>
<div class="line"><a name="l00024"></a><span class="lineno">   24</span>&#160;<span class="comment">// (hip_bfloat16.h), and they are not tagged constexpr</span></div>
<div class="line"><a name="l00025"></a><span class="lineno">   25</span>&#160;<span class="comment">// As a consequence, we get compile failures when compiling Eigen with</span></div>
<div class="line"><a name="l00026"></a><span class="lineno">   26</span>&#160;<span class="comment">// GPU support. Hence the need to disable EIGEN_CONSTEXPR when building</span></div>
<div class="line"><a name="l00027"></a><span class="lineno">   27</span>&#160;<span class="comment">// Eigen with GPU support</span></div>
<div class="line"><a name="l00028"></a><span class="lineno">   28</span>&#160;<span class="preprocessor">  #pragma push_macro(&quot;EIGEN_CONSTEXPR&quot;</span>)</div>
<div class="line"><a name="l00029"></a><span class="lineno">   29</span>&#160;<span class="preprocessor">  #undef EIGEN_CONSTEXPR</span></div>
<div class="line"><a name="l00030"></a><span class="lineno">   30</span>&#160;<span class="preprocessor">  #define EIGEN_CONSTEXPR</span></div>
<div class="line"><a name="l00031"></a><span class="lineno">   31</span>&#160;<span class="preprocessor">#endif</span></div>
<div class="line"><a name="l00032"></a><span class="lineno">   32</span>&#160; </div>
<div class="line"><a name="l00033"></a><span class="lineno">   33</span>&#160;<span class="preprocessor">#define BF16_PACKET_FUNCTION(PACKET_F, PACKET_BF16, METHOD)         \</span></div>
<div class="line"><a name="l00034"></a><span class="lineno">   34</span>&#160;<span class="preprocessor">  template &lt;&gt;                                                       \</span></div>
<div class="line"><a name="l00035"></a><span class="lineno">   35</span>&#160;<span class="preprocessor">  EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS EIGEN_UNUSED  \</span></div>
<div class="line"><a name="l00036"></a><span class="lineno">   36</span>&#160;<span class="preprocessor">  PACKET_BF16 METHOD&lt;PACKET_BF16&gt;(const PACKET_BF16&amp; _x) {          \</span></div>
<div class="line"><a name="l00037"></a><span class="lineno">   37</span>&#160;<span class="preprocessor">    return F32ToBf16(METHOD&lt;PACKET_F&gt;(Bf16ToF32(_x)));              \</span></div>
<div class="line"><a name="l00038"></a><span class="lineno">   38</span>&#160;<span class="preprocessor">  }</span></div>
<div class="line"><a name="l00039"></a><span class="lineno">   39</span>&#160; </div>
<div class="line"><a name="l00040"></a><span class="lineno">   40</span>&#160;<span class="comment">// Only use HIP GPU bf16 in kernels</span></div>
<div class="line"><a name="l00041"></a><span class="lineno">   41</span>&#160;<span class="preprocessor">#if defined(EIGEN_HAS_HIP_BF16) &amp;&amp; defined(EIGEN_GPU_COMPILE_PHASE)</span></div>
<div class="line"><a name="l00042"></a><span class="lineno">   42</span>&#160;<span class="preprocessor">#define EIGEN_USE_HIP_BF16</span></div>
<div class="line"><a name="l00043"></a><span class="lineno">   43</span>&#160;<span class="preprocessor">#endif</span></div>
<div class="line"><a name="l00044"></a><span class="lineno">   44</span>&#160; </div>
<div class="line"><a name="l00045"></a><span class="lineno">   45</span>&#160;<span class="keyword">namespace </span><a class="code" href="namespaceEigen.html">Eigen</a> {</div>
<div class="line"><a name="l00046"></a><span class="lineno">   46</span>&#160; </div>
<div class="line"><a name="l00047"></a><span class="lineno">   47</span>&#160;<span class="keyword">struct </span>bfloat16;</div>
<div class="line"><a name="l00048"></a><span class="lineno">   48</span>&#160; </div>
<div class="line"><a name="l00049"></a><span class="lineno">   49</span>&#160;<span class="keyword">namespace </span>numext {</div>
<div class="line"><a name="l00050"></a><span class="lineno">   50</span>&#160;<span class="keyword">template</span> &lt;&gt;</div>
<div class="line"><a name="l00051"></a><span class="lineno">   51</span>&#160;EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC Eigen::bfloat16 bit_cast&lt;Eigen::bfloat16, uint16_t&gt;(<span class="keyword">const</span> uint16_t&amp; src);</div>
<div class="line"><a name="l00052"></a><span class="lineno">   52</span>&#160; </div>
<div class="line"><a name="l00053"></a><span class="lineno">   53</span>&#160;<span class="keyword">template</span> &lt;&gt;</div>
<div class="line"><a name="l00054"></a><span class="lineno">   54</span>&#160;EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC uint16_t bit_cast&lt;uint16_t, Eigen::bfloat16&gt;(<span class="keyword">const</span> Eigen::bfloat16&amp; src);</div>
<div class="line"><a name="l00055"></a><span class="lineno">   55</span>&#160;}  <span class="comment">// namespace numext</span></div>
<div class="line"><a name="l00056"></a><span class="lineno">   56</span>&#160;<span class="keyword">namespace </span>bfloat16_impl {</div>
<div class="line"><a name="l00057"></a><span class="lineno">   57</span>&#160; </div>
<div class="line"><a name="l00058"></a><span class="lineno">   58</span>&#160;<span class="preprocessor">#if defined(EIGEN_USE_HIP_BF16)</span></div>
<div class="line"><a name="l00059"></a><span class="lineno">   59</span>&#160; </div>
<div class="line"><a name="l00060"></a><span class="lineno">   60</span>&#160;<span class="keyword">struct </span>__bfloat16_raw : <span class="keyword">public</span> hip_bfloat16 {</div>
<div class="line"><a name="l00061"></a><span class="lineno">   61</span>&#160;  EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR __bfloat16_raw() {}</div>
<div class="line"><a name="l00062"></a><span class="lineno">   62</span>&#160;  EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR __bfloat16_raw(hip_bfloat16 hb) : hip_bfloat16(hb) {}</div>
<div class="line"><a name="l00063"></a><span class="lineno">   63</span>&#160;  <span class="keyword">explicit</span> EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR __bfloat16_raw(<span class="keywordtype">unsigned</span> <span class="keywordtype">short</span> raw) : hip_bfloat16(raw) {}</div>
<div class="line"><a name="l00064"></a><span class="lineno">   64</span>&#160;};</div>
<div class="line"><a name="l00065"></a><span class="lineno">   65</span>&#160; </div>
<div class="line"><a name="l00066"></a><span class="lineno">   66</span>&#160;<span class="preprocessor">#else</span></div>
<div class="line"><a name="l00067"></a><span class="lineno">   67</span>&#160; </div>
<div class="line"><a name="l00068"></a><span class="lineno">   68</span>&#160;<span class="comment">// Make our own __bfloat16_raw definition.</span></div>
<div class="line"><a name="l00069"></a><span class="lineno">   69</span>&#160;<span class="keyword">struct </span>__bfloat16_raw {</div>
<div class="line"><a name="l00070"></a><span class="lineno">   70</span>&#160;<span class="preprocessor">#if defined(EIGEN_HAS_HIP_BF16) &amp;&amp; !defined(EIGEN_GPU_COMPILE_PHASE)</span></div>
<div class="line"><a name="l00071"></a><span class="lineno">   71</span>&#160;  EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR __bfloat16_raw() {}</div>
<div class="line"><a name="l00072"></a><span class="lineno">   72</span>&#160;<span class="preprocessor">#else</span></div>
<div class="line"><a name="l00073"></a><span class="lineno">   73</span>&#160;  EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR __bfloat16_raw() : value(0) {}</div>
<div class="line"><a name="l00074"></a><span class="lineno">   74</span>&#160;<span class="preprocessor">#endif</span></div>
<div class="line"><a name="l00075"></a><span class="lineno">   75</span>&#160;  <span class="keyword">explicit</span> EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR __bfloat16_raw(<span class="keywordtype">unsigned</span> <span class="keywordtype">short</span> raw) : value(raw) {}</div>
<div class="line"><a name="l00076"></a><span class="lineno">   76</span>&#160;  <span class="keywordtype">unsigned</span> <span class="keywordtype">short</span> value;</div>
<div class="line"><a name="l00077"></a><span class="lineno">   77</span>&#160;};</div>
<div class="line"><a name="l00078"></a><span class="lineno">   78</span>&#160; </div>
<div class="line"><a name="l00079"></a><span class="lineno">   79</span>&#160;<span class="preprocessor">#endif </span><span class="comment">// defined(EIGEN_USE_HIP_BF16)</span></div>
<div class="line"><a name="l00080"></a><span class="lineno">   80</span>&#160; </div>
<div class="line"><a name="l00081"></a><span class="lineno">   81</span>&#160;EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR __bfloat16_raw raw_uint16_to_bfloat16(<span class="keywordtype">unsigned</span> <span class="keywordtype">short</span> value);</div>
<div class="line"><a name="l00082"></a><span class="lineno">   82</span>&#160;<span class="keyword">template</span> &lt;<span class="keywordtype">bool</span> AssumeArgumentIsNormalOrInfinityOrZero&gt;</div>
<div class="line"><a name="l00083"></a><span class="lineno">   83</span>&#160;EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC __bfloat16_raw float_to_bfloat16_rtne(<span class="keywordtype">float</span> ff);</div>
<div class="line"><a name="l00084"></a><span class="lineno">   84</span>&#160;<span class="comment">// Forward declarations of template specializations, to avoid Visual C++ 2019 errors, saying:</span></div>
<div class="line"><a name="l00085"></a><span class="lineno">   85</span>&#160;<span class="comment">// &gt; error C2908: explicit specialization; &#39;float_to_bfloat16_rtne&#39; has already been instantiated</span></div>
<div class="line"><a name="l00086"></a><span class="lineno">   86</span>&#160;<span class="keyword">template</span> &lt;&gt;</div>
<div class="line"><a name="l00087"></a><span class="lineno">   87</span>&#160;EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC __bfloat16_raw float_to_bfloat16_rtne&lt;false&gt;(<span class="keywordtype">float</span> ff);</div>
<div class="line"><a name="l00088"></a><span class="lineno">   88</span>&#160;<span class="keyword">template</span> &lt;&gt;</div>
<div class="line"><a name="l00089"></a><span class="lineno">   89</span>&#160;EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC __bfloat16_raw float_to_bfloat16_rtne&lt;true&gt;(<span class="keywordtype">float</span> ff);</div>
<div class="line"><a name="l00090"></a><span class="lineno">   90</span>&#160;EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC <span class="keywordtype">float</span> bfloat16_to_float(__bfloat16_raw h);</div>
<div class="line"><a name="l00091"></a><span class="lineno">   91</span>&#160; </div>
<div class="line"><a name="l00092"></a><span class="lineno">   92</span>&#160;<span class="keyword">struct </span>bfloat16_base : <span class="keyword">public</span> __bfloat16_raw {</div>
<div class="line"><a name="l00093"></a><span class="lineno">   93</span>&#160;  EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR bfloat16_base() {}</div>
<div class="line"><a name="l00094"></a><span class="lineno">   94</span>&#160;  EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR bfloat16_base(<span class="keyword">const</span> __bfloat16_raw&amp; h) : __bfloat16_raw(h) {}</div>
<div class="line"><a name="l00095"></a><span class="lineno">   95</span>&#160;};</div>
<div class="line"><a name="l00096"></a><span class="lineno">   96</span>&#160; </div>
<div class="line"><a name="l00097"></a><span class="lineno">   97</span>&#160;} <span class="comment">// namespace bfloat16_impl</span></div>
<div class="line"><a name="l00098"></a><span class="lineno">   98</span>&#160; </div>
<div class="line"><a name="l00099"></a><span class="lineno">   99</span>&#160;<span class="comment">// Class definition.</span></div>
<div class="line"><a name="l00100"></a><span class="lineno">  100</span>&#160;<span class="keyword">struct </span>bfloat16 : <span class="keyword">public</span> bfloat16_impl::bfloat16_base {</div>
<div class="line"><a name="l00101"></a><span class="lineno">  101</span>&#160; </div>
<div class="line"><a name="l00102"></a><span class="lineno">  102</span>&#160;  <span class="keyword">typedef</span> bfloat16_impl::__bfloat16_raw __bfloat16_raw;</div>
<div class="line"><a name="l00103"></a><span class="lineno">  103</span>&#160; </div>
<div class="line"><a name="l00104"></a><span class="lineno">  104</span>&#160;  EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR bfloat16() {}</div>
<div class="line"><a name="l00105"></a><span class="lineno">  105</span>&#160; </div>
<div class="line"><a name="l00106"></a><span class="lineno">  106</span>&#160;  EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR bfloat16(<span class="keyword">const</span> __bfloat16_raw&amp; h) : bfloat16_impl::bfloat16_base(h) {}</div>
<div class="line"><a name="l00107"></a><span class="lineno">  107</span>&#160; </div>
<div class="line"><a name="l00108"></a><span class="lineno">  108</span>&#160;  <span class="keyword">explicit</span> EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR bfloat16(<span class="keywordtype">bool</span> b)</div>
<div class="line"><a name="l00109"></a><span class="lineno">  109</span>&#160;      : bfloat16_impl::bfloat16_base(bfloat16_impl::raw_uint16_to_bfloat16(b ? 0x3f80 : 0)) {}</div>
<div class="line"><a name="l00110"></a><span class="lineno">  110</span>&#160; </div>
<div class="line"><a name="l00111"></a><span class="lineno">  111</span>&#160;  <span class="keyword">template</span>&lt;<span class="keyword">class</span> T&gt;</div>
<div class="line"><a name="l00112"></a><span class="lineno">  112</span>&#160;  <span class="keyword">explicit</span> EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR bfloat16(T val)</div>
<div class="line"><a name="l00113"></a><span class="lineno">  113</span>&#160;      : bfloat16_impl::bfloat16_base(bfloat16_impl::float_to_bfloat16_rtne&lt;internal::is_integral&lt;T&gt;::value&gt;(static_cast&lt;float&gt;(val))) {}</div>
<div class="line"><a name="l00114"></a><span class="lineno">  114</span>&#160; </div>
<div class="line"><a name="l00115"></a><span class="lineno">  115</span>&#160;  <span class="keyword">explicit</span> EIGEN_DEVICE_FUNC bfloat16(<span class="keywordtype">float</span> f)</div>
<div class="line"><a name="l00116"></a><span class="lineno">  116</span>&#160;      : bfloat16_impl::bfloat16_base(bfloat16_impl::float_to_bfloat16_rtne&lt;false&gt;(f)) {}</div>
<div class="line"><a name="l00117"></a><span class="lineno">  117</span>&#160; </div>
<div class="line"><a name="l00118"></a><span class="lineno">  118</span>&#160;  <span class="comment">// Following the convention of numpy, converting between complex and</span></div>
<div class="line"><a name="l00119"></a><span class="lineno">  119</span>&#160;  <span class="comment">// float will lead to loss of imag value.</span></div>
<div class="line"><a name="l00120"></a><span class="lineno">  120</span>&#160;  <span class="keyword">template</span>&lt;<span class="keyword">typename</span> RealScalar&gt;</div>
<div class="line"><a name="l00121"></a><span class="lineno">  121</span>&#160;  <span class="keyword">explicit</span> EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR bfloat16(<span class="keyword">const</span> std::complex&lt;RealScalar&gt;&amp; val)</div>
<div class="line"><a name="l00122"></a><span class="lineno">  122</span>&#160;      : bfloat16_impl::bfloat16_base(bfloat16_impl::float_to_bfloat16_rtne&lt;false&gt;(static_cast&lt;float&gt;(val.<a class="code" href="namespaceEigen.html#ac74dc920119b1eba45e9218d9f402afc">real</a>()))) {}</div>
<div class="line"><a name="l00123"></a><span class="lineno">  123</span>&#160; </div>
<div class="line"><a name="l00124"></a><span class="lineno">  124</span>&#160;  EIGEN_DEVICE_FUNC <span class="keyword">operator</span> float()<span class="keyword"> const </span>{  <span class="comment">// NOLINT: Allow implicit conversion to float, because it is lossless.</span></div>
<div class="line"><a name="l00125"></a><span class="lineno">  125</span>&#160;    <span class="keywordflow">return</span> bfloat16_impl::bfloat16_to_float(*<span class="keyword">this</span>);</div>
<div class="line"><a name="l00126"></a><span class="lineno">  126</span>&#160;  }</div>
<div class="line"><a name="l00127"></a><span class="lineno">  127</span>&#160;};</div>
<div class="line"><a name="l00128"></a><span class="lineno">  128</span>&#160; </div>
<div class="line"><a name="l00129"></a><span class="lineno">  129</span>&#160;<span class="comment">// TODO(majnemer): Get rid of this once we can rely on C++17 inline variables do</span></div>
<div class="line"><a name="l00130"></a><span class="lineno">  130</span>&#160;<span class="comment">// solve the ODR issue.</span></div>
<div class="line"><a name="l00131"></a><span class="lineno">  131</span>&#160;<span class="keyword">namespace </span>bfloat16_impl {</div>
<div class="line"><a name="l00132"></a><span class="lineno">  132</span>&#160;<span class="keyword">template</span> &lt;<span class="keyword">typename</span> = <span class="keywordtype">void</span>&gt;</div>
<div class="line"><a name="l00133"></a><span class="lineno">  133</span>&#160;<span class="keyword">struct </span>numeric_limits_bfloat16_impl {</div>
<div class="line"><a name="l00134"></a><span class="lineno">  134</span>&#160;  <span class="keyword">static</span> EIGEN_CONSTEXPR <span class="keyword">const</span> <span class="keywordtype">bool</span> is_specialized = <span class="keyword">true</span>;</div>
<div class="line"><a name="l00135"></a><span class="lineno">  135</span>&#160;  <span class="keyword">static</span> EIGEN_CONSTEXPR <span class="keyword">const</span> <span class="keywordtype">bool</span> is_signed = <span class="keyword">true</span>;</div>
<div class="line"><a name="l00136"></a><span class="lineno">  136</span>&#160;  <span class="keyword">static</span> EIGEN_CONSTEXPR <span class="keyword">const</span> <span class="keywordtype">bool</span> is_integer = <span class="keyword">false</span>;</div>
<div class="line"><a name="l00137"></a><span class="lineno">  137</span>&#160;  <span class="keyword">static</span> EIGEN_CONSTEXPR <span class="keyword">const</span> <span class="keywordtype">bool</span> is_exact = <span class="keyword">false</span>;</div>
<div class="line"><a name="l00138"></a><span class="lineno">  138</span>&#160;  <span class="keyword">static</span> EIGEN_CONSTEXPR <span class="keyword">const</span> <span class="keywordtype">bool</span> has_infinity = <span class="keyword">true</span>;</div>
<div class="line"><a name="l00139"></a><span class="lineno">  139</span>&#160;  <span class="keyword">static</span> EIGEN_CONSTEXPR <span class="keyword">const</span> <span class="keywordtype">bool</span> has_quiet_NaN = <span class="keyword">true</span>;</div>
<div class="line"><a name="l00140"></a><span class="lineno">  140</span>&#160;  <span class="keyword">static</span> EIGEN_CONSTEXPR <span class="keyword">const</span> <span class="keywordtype">bool</span> has_signaling_NaN = <span class="keyword">true</span>;</div>
<div class="line"><a name="l00141"></a><span class="lineno">  141</span>&#160;  <span class="keyword">static</span> EIGEN_CONSTEXPR <span class="keyword">const</span> std::float_denorm_style has_denorm = std::denorm_present;</div>
<div class="line"><a name="l00142"></a><span class="lineno">  142</span>&#160;  <span class="keyword">static</span> EIGEN_CONSTEXPR <span class="keyword">const</span> <span class="keywordtype">bool</span> has_denorm_loss = <span class="keyword">false</span>;</div>
<div class="line"><a name="l00143"></a><span class="lineno">  143</span>&#160;  <span class="keyword">static</span> EIGEN_CONSTEXPR <span class="keyword">const</span> std::float_round_style round_style = std::numeric_limits&lt;float&gt;::round_style;</div>
<div class="line"><a name="l00144"></a><span class="lineno">  144</span>&#160;  <span class="keyword">static</span> EIGEN_CONSTEXPR <span class="keyword">const</span> <span class="keywordtype">bool</span> is_iec559 = <span class="keyword">true</span>;</div>
<div class="line"><a name="l00145"></a><span class="lineno">  145</span>&#160;  <span class="comment">// The C++ standard defines this as &quot;true if the set of values representable</span></div>
<div class="line"><a name="l00146"></a><span class="lineno">  146</span>&#160;  <span class="comment">// by the type is finite.&quot; BFloat16 has finite precision.</span></div>
<div class="line"><a name="l00147"></a><span class="lineno">  147</span>&#160;  <span class="keyword">static</span> EIGEN_CONSTEXPR <span class="keyword">const</span> <span class="keywordtype">bool</span> is_bounded = <span class="keyword">true</span>;</div>
<div class="line"><a name="l00148"></a><span class="lineno">  148</span>&#160;  <span class="keyword">static</span> EIGEN_CONSTEXPR <span class="keyword">const</span> <span class="keywordtype">bool</span> is_modulo = <span class="keyword">false</span>;</div>
<div class="line"><a name="l00149"></a><span class="lineno">  149</span>&#160;  <span class="keyword">static</span> EIGEN_CONSTEXPR <span class="keyword">const</span> <span class="keywordtype">int</span> digits = 8;</div>
<div class="line"><a name="l00150"></a><span class="lineno">  150</span>&#160;  <span class="keyword">static</span> EIGEN_CONSTEXPR <span class="keyword">const</span> <span class="keywordtype">int</span> digits10 = 2;</div>
<div class="line"><a name="l00151"></a><span class="lineno">  151</span>&#160;  <span class="keyword">static</span> EIGEN_CONSTEXPR <span class="keyword">const</span> <span class="keywordtype">int</span> max_digits10 = 4;</div>
<div class="line"><a name="l00152"></a><span class="lineno">  152</span>&#160;  <span class="keyword">static</span> EIGEN_CONSTEXPR <span class="keyword">const</span> <span class="keywordtype">int</span> radix = std::numeric_limits&lt;float&gt;::radix;</div>
<div class="line"><a name="l00153"></a><span class="lineno">  153</span>&#160;  <span class="keyword">static</span> EIGEN_CONSTEXPR <span class="keyword">const</span> <span class="keywordtype">int</span> min_exponent = std::numeric_limits&lt;float&gt;::min_exponent;</div>
<div class="line"><a name="l00154"></a><span class="lineno">  154</span>&#160;  <span class="keyword">static</span> EIGEN_CONSTEXPR <span class="keyword">const</span> <span class="keywordtype">int</span> min_exponent10 = std::numeric_limits&lt;float&gt;::min_exponent10;</div>
<div class="line"><a name="l00155"></a><span class="lineno">  155</span>&#160;  <span class="keyword">static</span> EIGEN_CONSTEXPR <span class="keyword">const</span> <span class="keywordtype">int</span> max_exponent = std::numeric_limits&lt;float&gt;::max_exponent;</div>
<div class="line"><a name="l00156"></a><span class="lineno">  156</span>&#160;  <span class="keyword">static</span> EIGEN_CONSTEXPR <span class="keyword">const</span> <span class="keywordtype">int</span> max_exponent10 = std::numeric_limits&lt;float&gt;::max_exponent10;</div>
<div class="line"><a name="l00157"></a><span class="lineno">  157</span>&#160;  <span class="keyword">static</span> EIGEN_CONSTEXPR <span class="keyword">const</span> <span class="keywordtype">bool</span> traps = std::numeric_limits&lt;float&gt;::traps;</div>
<div class="line"><a name="l00158"></a><span class="lineno">  158</span>&#160;  <span class="comment">// IEEE754: &quot;The implementer shall choose how tininess is detected, but shall</span></div>
<div class="line"><a name="l00159"></a><span class="lineno">  159</span>&#160;  <span class="comment">// detect tininess in the same way for all operations in radix two&quot;</span></div>
<div class="line"><a name="l00160"></a><span class="lineno">  160</span>&#160;  <span class="keyword">static</span> EIGEN_CONSTEXPR <span class="keyword">const</span> <span class="keywordtype">bool</span> tinyness_before = std::numeric_limits&lt;float&gt;::tinyness_before;</div>
<div class="line"><a name="l00161"></a><span class="lineno">  161</span>&#160; </div>
<div class="line"><a name="l00162"></a><span class="lineno">  162</span>&#160;  <span class="keyword">static</span> EIGEN_CONSTEXPR Eigen::bfloat16 (min)() { <span class="keywordflow">return</span> Eigen::bfloat16_impl::raw_uint16_to_bfloat16(0x0080); }</div>
<div class="line"><a name="l00163"></a><span class="lineno">  163</span>&#160;  <span class="keyword">static</span> EIGEN_CONSTEXPR Eigen::bfloat16 lowest() { <span class="keywordflow">return</span> Eigen::bfloat16_impl::raw_uint16_to_bfloat16(0xff7f); }</div>
<div class="line"><a name="l00164"></a><span class="lineno">  164</span>&#160;  <span class="keyword">static</span> EIGEN_CONSTEXPR Eigen::bfloat16 (max)() { <span class="keywordflow">return</span> Eigen::bfloat16_impl::raw_uint16_to_bfloat16(0x7f7f); }</div>
<div class="line"><a name="l00165"></a><span class="lineno">  165</span>&#160;  <span class="keyword">static</span> EIGEN_CONSTEXPR Eigen::bfloat16 epsilon() { <span class="keywordflow">return</span> Eigen::bfloat16_impl::raw_uint16_to_bfloat16(0x3c00); }</div>
<div class="line"><a name="l00166"></a><span class="lineno">  166</span>&#160;  <span class="keyword">static</span> EIGEN_CONSTEXPR Eigen::bfloat16 round_error() { <span class="keywordflow">return</span> Eigen::bfloat16_impl::raw_uint16_to_bfloat16(0x3f00); }</div>
<div class="line"><a name="l00167"></a><span class="lineno">  167</span>&#160;  <span class="keyword">static</span> EIGEN_CONSTEXPR Eigen::bfloat16 infinity() { <span class="keywordflow">return</span> Eigen::bfloat16_impl::raw_uint16_to_bfloat16(0x7f80); }</div>
<div class="line"><a name="l00168"></a><span class="lineno">  168</span>&#160;  <span class="keyword">static</span> EIGEN_CONSTEXPR Eigen::bfloat16 quiet_NaN() { <span class="keywordflow">return</span> Eigen::bfloat16_impl::raw_uint16_to_bfloat16(0x7fc0); }</div>
<div class="line"><a name="l00169"></a><span class="lineno">  169</span>&#160;  <span class="keyword">static</span> EIGEN_CONSTEXPR Eigen::bfloat16 signaling_NaN() { <span class="keywordflow">return</span> Eigen::bfloat16_impl::raw_uint16_to_bfloat16(0x7fa0); }</div>
<div class="line"><a name="l00170"></a><span class="lineno">  170</span>&#160;  <span class="keyword">static</span> EIGEN_CONSTEXPR Eigen::bfloat16 denorm_min() { <span class="keywordflow">return</span> Eigen::bfloat16_impl::raw_uint16_to_bfloat16(0x0001); }</div>
<div class="line"><a name="l00171"></a><span class="lineno">  171</span>&#160;};</div>
<div class="line"><a name="l00172"></a><span class="lineno">  172</span>&#160; </div>
<div class="line"><a name="l00173"></a><span class="lineno">  173</span>&#160;<span class="keyword">template</span>&lt;<span class="keyword">typename</span> T&gt;</div>
<div class="line"><a name="l00174"></a><span class="lineno">  174</span>&#160;EIGEN_CONSTEXPR <span class="keyword">const</span> <span class="keywordtype">bool</span> numeric_limits_bfloat16_impl&lt;T&gt;::is_specialized;</div>
<div class="line"><a name="l00175"></a><span class="lineno">  175</span>&#160;<span class="keyword">template</span>&lt;<span class="keyword">typename</span> T&gt;</div>
<div class="line"><a name="l00176"></a><span class="lineno">  176</span>&#160;EIGEN_CONSTEXPR <span class="keyword">const</span> <span class="keywordtype">bool</span> numeric_limits_bfloat16_impl&lt;T&gt;::is_signed;</div>
<div class="line"><a name="l00177"></a><span class="lineno">  177</span>&#160;<span class="keyword">template</span>&lt;<span class="keyword">typename</span> T&gt;</div>
<div class="line"><a name="l00178"></a><span class="lineno">  178</span>&#160;EIGEN_CONSTEXPR <span class="keyword">const</span> <span class="keywordtype">bool</span> numeric_limits_bfloat16_impl&lt;T&gt;::is_integer;</div>
<div class="line"><a name="l00179"></a><span class="lineno">  179</span>&#160;<span class="keyword">template</span>&lt;<span class="keyword">typename</span> T&gt;</div>
<div class="line"><a name="l00180"></a><span class="lineno">  180</span>&#160;EIGEN_CONSTEXPR <span class="keyword">const</span> <span class="keywordtype">bool</span> numeric_limits_bfloat16_impl&lt;T&gt;::is_exact;</div>
<div class="line"><a name="l00181"></a><span class="lineno">  181</span>&#160;<span class="keyword">template</span>&lt;<span class="keyword">typename</span> T&gt;</div>
<div class="line"><a name="l00182"></a><span class="lineno">  182</span>&#160;EIGEN_CONSTEXPR <span class="keyword">const</span> <span class="keywordtype">bool</span> numeric_limits_bfloat16_impl&lt;T&gt;::has_infinity;</div>
<div class="line"><a name="l00183"></a><span class="lineno">  183</span>&#160;<span class="keyword">template</span>&lt;<span class="keyword">typename</span> T&gt;</div>
<div class="line"><a name="l00184"></a><span class="lineno">  184</span>&#160;EIGEN_CONSTEXPR <span class="keyword">const</span> <span class="keywordtype">bool</span> numeric_limits_bfloat16_impl&lt;T&gt;::has_quiet_NaN;</div>
<div class="line"><a name="l00185"></a><span class="lineno">  185</span>&#160;<span class="keyword">template</span>&lt;<span class="keyword">typename</span> T&gt;</div>
<div class="line"><a name="l00186"></a><span class="lineno">  186</span>&#160;EIGEN_CONSTEXPR <span class="keyword">const</span> <span class="keywordtype">bool</span> numeric_limits_bfloat16_impl&lt;T&gt;::has_signaling_NaN;</div>
<div class="line"><a name="l00187"></a><span class="lineno">  187</span>&#160;<span class="keyword">template</span>&lt;<span class="keyword">typename</span> T&gt;</div>
<div class="line"><a name="l00188"></a><span class="lineno">  188</span>&#160;EIGEN_CONSTEXPR <span class="keyword">const</span> std::float_denorm_style numeric_limits_bfloat16_impl&lt;T&gt;::has_denorm;</div>
<div class="line"><a name="l00189"></a><span class="lineno">  189</span>&#160;<span class="keyword">template</span>&lt;<span class="keyword">typename</span> T&gt;</div>
<div class="line"><a name="l00190"></a><span class="lineno">  190</span>&#160;EIGEN_CONSTEXPR <span class="keyword">const</span> <span class="keywordtype">bool</span> numeric_limits_bfloat16_impl&lt;T&gt;::has_denorm_loss;</div>
<div class="line"><a name="l00191"></a><span class="lineno">  191</span>&#160;<span class="keyword">template</span>&lt;<span class="keyword">typename</span> T&gt;</div>
<div class="line"><a name="l00192"></a><span class="lineno">  192</span>&#160;EIGEN_CONSTEXPR <span class="keyword">const</span> std::float_round_style numeric_limits_bfloat16_impl&lt;T&gt;::round_style;</div>
<div class="line"><a name="l00193"></a><span class="lineno">  193</span>&#160;<span class="keyword">template</span>&lt;<span class="keyword">typename</span> T&gt;</div>
<div class="line"><a name="l00194"></a><span class="lineno">  194</span>&#160;EIGEN_CONSTEXPR <span class="keyword">const</span> <span class="keywordtype">bool</span> numeric_limits_bfloat16_impl&lt;T&gt;::is_iec559;</div>
<div class="line"><a name="l00195"></a><span class="lineno">  195</span>&#160;<span class="keyword">template</span>&lt;<span class="keyword">typename</span> T&gt;</div>
<div class="line"><a name="l00196"></a><span class="lineno">  196</span>&#160;EIGEN_CONSTEXPR <span class="keyword">const</span> <span class="keywordtype">bool</span> numeric_limits_bfloat16_impl&lt;T&gt;::is_bounded;</div>
<div class="line"><a name="l00197"></a><span class="lineno">  197</span>&#160;<span class="keyword">template</span>&lt;<span class="keyword">typename</span> T&gt;</div>
<div class="line"><a name="l00198"></a><span class="lineno">  198</span>&#160;EIGEN_CONSTEXPR <span class="keyword">const</span> <span class="keywordtype">bool</span> numeric_limits_bfloat16_impl&lt;T&gt;::is_modulo;</div>
<div class="line"><a name="l00199"></a><span class="lineno">  199</span>&#160;<span class="keyword">template</span>&lt;<span class="keyword">typename</span> T&gt;</div>
<div class="line"><a name="l00200"></a><span class="lineno">  200</span>&#160;EIGEN_CONSTEXPR <span class="keyword">const</span> <span class="keywordtype">int</span> numeric_limits_bfloat16_impl&lt;T&gt;::digits;</div>
<div class="line"><a name="l00201"></a><span class="lineno">  201</span>&#160;<span class="keyword">template</span>&lt;<span class="keyword">typename</span> T&gt;</div>
<div class="line"><a name="l00202"></a><span class="lineno">  202</span>&#160;EIGEN_CONSTEXPR <span class="keyword">const</span> <span class="keywordtype">int</span> numeric_limits_bfloat16_impl&lt;T&gt;::digits10;</div>
<div class="line"><a name="l00203"></a><span class="lineno">  203</span>&#160;<span class="keyword">template</span>&lt;<span class="keyword">typename</span> T&gt;</div>
<div class="line"><a name="l00204"></a><span class="lineno">  204</span>&#160;EIGEN_CONSTEXPR <span class="keyword">const</span> <span class="keywordtype">int</span> numeric_limits_bfloat16_impl&lt;T&gt;::max_digits10;</div>
<div class="line"><a name="l00205"></a><span class="lineno">  205</span>&#160;<span class="keyword">template</span>&lt;<span class="keyword">typename</span> T&gt;</div>
<div class="line"><a name="l00206"></a><span class="lineno">  206</span>&#160;EIGEN_CONSTEXPR <span class="keyword">const</span> <span class="keywordtype">int</span> numeric_limits_bfloat16_impl&lt;T&gt;::radix;</div>
<div class="line"><a name="l00207"></a><span class="lineno">  207</span>&#160;<span class="keyword">template</span>&lt;<span class="keyword">typename</span> T&gt;</div>
<div class="line"><a name="l00208"></a><span class="lineno">  208</span>&#160;EIGEN_CONSTEXPR <span class="keyword">const</span> <span class="keywordtype">int</span> numeric_limits_bfloat16_impl&lt;T&gt;::min_exponent;</div>
<div class="line"><a name="l00209"></a><span class="lineno">  209</span>&#160;<span class="keyword">template</span>&lt;<span class="keyword">typename</span> T&gt;</div>
<div class="line"><a name="l00210"></a><span class="lineno">  210</span>&#160;EIGEN_CONSTEXPR <span class="keyword">const</span> <span class="keywordtype">int</span> numeric_limits_bfloat16_impl&lt;T&gt;::min_exponent10;</div>
<div class="line"><a name="l00211"></a><span class="lineno">  211</span>&#160;<span class="keyword">template</span>&lt;<span class="keyword">typename</span> T&gt;</div>
<div class="line"><a name="l00212"></a><span class="lineno">  212</span>&#160;EIGEN_CONSTEXPR <span class="keyword">const</span> <span class="keywordtype">int</span> numeric_limits_bfloat16_impl&lt;T&gt;::max_exponent;</div>
<div class="line"><a name="l00213"></a><span class="lineno">  213</span>&#160;<span class="keyword">template</span>&lt;<span class="keyword">typename</span> T&gt;</div>
<div class="line"><a name="l00214"></a><span class="lineno">  214</span>&#160;EIGEN_CONSTEXPR <span class="keyword">const</span> <span class="keywordtype">int</span> numeric_limits_bfloat16_impl&lt;T&gt;::max_exponent10;</div>
<div class="line"><a name="l00215"></a><span class="lineno">  215</span>&#160;<span class="keyword">template</span>&lt;<span class="keyword">typename</span> T&gt;</div>
<div class="line"><a name="l00216"></a><span class="lineno">  216</span>&#160;EIGEN_CONSTEXPR <span class="keyword">const</span> <span class="keywordtype">bool</span> numeric_limits_bfloat16_impl&lt;T&gt;::traps;</div>
<div class="line"><a name="l00217"></a><span class="lineno">  217</span>&#160;<span class="keyword">template</span>&lt;<span class="keyword">typename</span> T&gt;</div>
<div class="line"><a name="l00218"></a><span class="lineno">  218</span>&#160;EIGEN_CONSTEXPR <span class="keyword">const</span> <span class="keywordtype">bool</span> numeric_limits_bfloat16_impl&lt;T&gt;::tinyness_before;</div>
<div class="line"><a name="l00219"></a><span class="lineno">  219</span>&#160;}  <span class="comment">// end namespace bfloat16_impl</span></div>
<div class="line"><a name="l00220"></a><span class="lineno">  220</span>&#160;}  <span class="comment">// end namespace Eigen</span></div>
<div class="line"><a name="l00221"></a><span class="lineno">  221</span>&#160; </div>
<div class="line"><a name="l00222"></a><span class="lineno">  222</span>&#160;<span class="keyword">namespace </span>std {</div>
<div class="line"><a name="l00223"></a><span class="lineno">  223</span>&#160;<span class="comment">// If std::numeric_limits&lt;T&gt; is specialized, should also specialize</span></div>
<div class="line"><a name="l00224"></a><span class="lineno">  224</span>&#160;<span class="comment">// std::numeric_limits&lt;const T&gt;, std::numeric_limits&lt;volatile T&gt;, and</span></div>
<div class="line"><a name="l00225"></a><span class="lineno">  225</span>&#160;<span class="comment">// std::numeric_limits&lt;const volatile T&gt;</span></div>
<div class="line"><a name="l00226"></a><span class="lineno">  226</span>&#160;<span class="comment">// https://stackoverflow.com/a/16519653/</span></div>
<div class="line"><a name="l00227"></a><span class="lineno">  227</span>&#160;<span class="keyword">template</span>&lt;&gt;</div>
<div class="line"><a name="l00228"></a><span class="lineno">  228</span>&#160;<span class="keyword">class </span>numeric_limits&lt;<a class="code" href="namespaceEigen.html">Eigen</a>::bfloat16&gt; : <span class="keyword">public</span> Eigen::bfloat16_impl::numeric_limits_bfloat16_impl&lt;&gt; {};</div>
<div class="line"><a name="l00229"></a><span class="lineno">  229</span>&#160;<span class="keyword">template</span>&lt;&gt;</div>
<div class="line"><a name="l00230"></a><span class="lineno">  230</span>&#160;<span class="keyword">class </span>numeric_limits&lt;const <a class="code" href="namespaceEigen.html">Eigen</a>::bfloat16&gt; : <span class="keyword">public</span> numeric_limits&lt;Eigen::bfloat16&gt; {};</div>
<div class="line"><a name="l00231"></a><span class="lineno">  231</span>&#160;<span class="keyword">template</span>&lt;&gt;</div>
<div class="line"><a name="l00232"></a><span class="lineno">  232</span>&#160;<span class="keyword">class </span>numeric_limits&lt;volatile <a class="code" href="namespaceEigen.html">Eigen</a>::bfloat16&gt; : <span class="keyword">public</span> numeric_limits&lt;Eigen::bfloat16&gt; {};</div>
<div class="line"><a name="l00233"></a><span class="lineno">  233</span>&#160;<span class="keyword">template</span>&lt;&gt;</div>
<div class="line"><a name="l00234"></a><span class="lineno">  234</span>&#160;<span class="keyword">class </span>numeric_limits&lt;const volatile <a class="code" href="namespaceEigen.html">Eigen</a>::bfloat16&gt; : <span class="keyword">public</span> numeric_limits&lt;Eigen::bfloat16&gt; {};</div>
<div class="line"><a name="l00235"></a><span class="lineno">  235</span>&#160;}  <span class="comment">// end namespace std</span></div>
<div class="line"><a name="l00236"></a><span class="lineno">  236</span>&#160; </div>
<div class="line"><a name="l00237"></a><span class="lineno">  237</span>&#160;<span class="keyword">namespace </span><a class="code" href="namespaceEigen.html">Eigen</a> {</div>
<div class="line"><a name="l00238"></a><span class="lineno">  238</span>&#160; </div>
<div class="line"><a name="l00239"></a><span class="lineno">  239</span>&#160;<span class="keyword">namespace </span>bfloat16_impl {</div>
<div class="line"><a name="l00240"></a><span class="lineno">  240</span>&#160; </div>
<div class="line"><a name="l00241"></a><span class="lineno">  241</span>&#160;<span class="comment">// We need to distinguish ‘clang as the CUDA compiler’ from ‘clang as the host compiler,</span></div>
<div class="line"><a name="l00242"></a><span class="lineno">  242</span>&#160;<span class="comment">// invoked by NVCC’ (e.g. on MacOS). The former needs to see both host and device implementation</span></div>
<div class="line"><a name="l00243"></a><span class="lineno">  243</span>&#160;<span class="comment">// of the functions, while the latter can only deal with one of them.</span></div>
<div class="line"><a name="l00244"></a><span class="lineno">  244</span>&#160;<span class="preprocessor">#if !defined(EIGEN_HAS_NATIVE_BF16) || (EIGEN_COMP_CLANG &amp;&amp; !EIGEN_COMP_NVCC) </span><span class="comment">// Emulate support for bfloat16 floats</span></div>
<div class="line"><a name="l00245"></a><span class="lineno">  245</span>&#160; </div>
<div class="line"><a name="l00246"></a><span class="lineno">  246</span>&#160;<span class="preprocessor">#if EIGEN_COMP_CLANG &amp;&amp; defined(EIGEN_CUDACC)</span></div>
<div class="line"><a name="l00247"></a><span class="lineno">  247</span>&#160;<span class="comment">// We need to provide emulated *host-side* BF16 operators for clang.</span></div>
<div class="line"><a name="l00248"></a><span class="lineno">  248</span>&#160;<span class="preprocessor">#pragma push_macro(&quot;EIGEN_DEVICE_FUNC&quot;</span>)</div>
<div class="line"><a name="l00249"></a><span class="lineno">  249</span>&#160;<span class="preprocessor">#undef EIGEN_DEVICE_FUNC</span></div>
<div class="line"><a name="l00250"></a><span class="lineno">  250</span>&#160;<span class="preprocessor">#if (defined(EIGEN_HAS_GPU_BF16) &amp;&amp; defined(EIGEN_HAS_NATIVE_BF16))</span></div>
<div class="line"><a name="l00251"></a><span class="lineno">  251</span>&#160;<span class="preprocessor">#define EIGEN_DEVICE_FUNC __host__</span></div>
<div class="line"><a name="l00252"></a><span class="lineno">  252</span>&#160;<span class="preprocessor">#else </span><span class="comment">// both host and device need emulated ops.</span></div>
<div class="line"><a name="l00253"></a><span class="lineno">  253</span>&#160;<span class="preprocessor">#define EIGEN_DEVICE_FUNC __host__ __device__</span></div>
<div class="line"><a name="l00254"></a><span class="lineno">  254</span>&#160;<span class="preprocessor">#endif</span></div>
<div class="line"><a name="l00255"></a><span class="lineno">  255</span>&#160;<span class="preprocessor">#endif</span></div>
<div class="line"><a name="l00256"></a><span class="lineno">  256</span>&#160; </div>
<div class="line"><a name="l00257"></a><span class="lineno">  257</span>&#160;<span class="comment">// Definitions for CPUs, mostly working through conversion</span></div>
<div class="line"><a name="l00258"></a><span class="lineno">  258</span>&#160;<span class="comment">// to/from fp32.</span></div>
<div class="line"><a name="l00259"></a><span class="lineno">  259</span>&#160; </div>
<div class="line"><a name="l00260"></a><span class="lineno">  260</span>&#160;EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC bfloat16 operator + (<span class="keyword">const</span> bfloat16&amp; a, <span class="keyword">const</span> bfloat16&amp; b) {</div>
<div class="line"><a name="l00261"></a><span class="lineno">  261</span>&#160;  <span class="keywordflow">return</span> bfloat16(<span class="keywordtype">float</span>(a) + <span class="keywordtype">float</span>(b));</div>
<div class="line"><a name="l00262"></a><span class="lineno">  262</span>&#160;}</div>
<div class="line"><a name="l00263"></a><span class="lineno">  263</span>&#160;EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC bfloat16 operator + (<span class="keyword">const</span> bfloat16&amp; a, <span class="keyword">const</span> <span class="keywordtype">int</span>&amp; b) {</div>
<div class="line"><a name="l00264"></a><span class="lineno">  264</span>&#160;  <span class="keywordflow">return</span> bfloat16(<span class="keywordtype">float</span>(a) + <span class="keyword">static_cast&lt;</span><span class="keywordtype">float</span><span class="keyword">&gt;</span>(b));</div>
<div class="line"><a name="l00265"></a><span class="lineno">  265</span>&#160;}</div>
<div class="line"><a name="l00266"></a><span class="lineno">  266</span>&#160;EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC bfloat16 operator + (<span class="keyword">const</span> <span class="keywordtype">int</span>&amp; a, <span class="keyword">const</span> bfloat16&amp; b) {</div>
<div class="line"><a name="l00267"></a><span class="lineno">  267</span>&#160;  <span class="keywordflow">return</span> bfloat16(<span class="keyword">static_cast&lt;</span><span class="keywordtype">float</span><span class="keyword">&gt;</span>(a) + <span class="keywordtype">float</span>(b));</div>
<div class="line"><a name="l00268"></a><span class="lineno">  268</span>&#160;}</div>
<div class="line"><a name="l00269"></a><span class="lineno">  269</span>&#160;EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC bfloat16 <a class="code" href="namespaceEigen.html#a9723b3ff0f2c99fe1081e3eb14380d4c">operator * </a>(<span class="keyword">const</span> bfloat16&amp; a, <span class="keyword">const</span> bfloat16&amp; b) {</div>
<div class="line"><a name="l00270"></a><span class="lineno">  270</span>&#160;  <span class="keywordflow">return</span> bfloat16(<span class="keywordtype">float</span>(a) * <span class="keywordtype">float</span>(b));</div>
<div class="line"><a name="l00271"></a><span class="lineno">  271</span>&#160;}</div>
<div class="line"><a name="l00272"></a><span class="lineno">  272</span>&#160;EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC bfloat16 operator - (<span class="keyword">const</span> bfloat16&amp; a, <span class="keyword">const</span> bfloat16&amp; b) {</div>
<div class="line"><a name="l00273"></a><span class="lineno">  273</span>&#160;  <span class="keywordflow">return</span> bfloat16(<span class="keywordtype">float</span>(a) - <span class="keywordtype">float</span>(b));</div>
<div class="line"><a name="l00274"></a><span class="lineno">  274</span>&#160;}</div>
<div class="line"><a name="l00275"></a><span class="lineno">  275</span>&#160;EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC bfloat16 operator / (<span class="keyword">const</span> bfloat16&amp; a, <span class="keyword">const</span> bfloat16&amp; b) {</div>
<div class="line"><a name="l00276"></a><span class="lineno">  276</span>&#160;  <span class="keywordflow">return</span> bfloat16(<span class="keywordtype">float</span>(a) / <span class="keywordtype">float</span>(b));</div>
<div class="line"><a name="l00277"></a><span class="lineno">  277</span>&#160;}</div>
<div class="line"><a name="l00278"></a><span class="lineno">  278</span>&#160;EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC bfloat16 operator - (<span class="keyword">const</span> bfloat16&amp; a) {</div>
<div class="line"><a name="l00279"></a><span class="lineno">  279</span>&#160;  numext::uint16_t x = numext::bit_cast&lt;uint16_t&gt;(a) ^ 0x8000;</div>
<div class="line"><a name="l00280"></a><span class="lineno">  280</span>&#160;  <span class="keywordflow">return</span> numext::bit_cast&lt;bfloat16&gt;(x);</div>
<div class="line"><a name="l00281"></a><span class="lineno">  281</span>&#160;}</div>
<div class="line"><a name="l00282"></a><span class="lineno">  282</span>&#160;EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC bfloat16&amp; operator += (bfloat16&amp; a, <span class="keyword">const</span> bfloat16&amp; b) {</div>
<div class="line"><a name="l00283"></a><span class="lineno">  283</span>&#160;  a = bfloat16(<span class="keywordtype">float</span>(a) + <span class="keywordtype">float</span>(b));</div>
<div class="line"><a name="l00284"></a><span class="lineno">  284</span>&#160;  <span class="keywordflow">return</span> a;</div>
<div class="line"><a name="l00285"></a><span class="lineno">  285</span>&#160;}</div>
<div class="line"><a name="l00286"></a><span class="lineno">  286</span>&#160;EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC bfloat16&amp; operator *= (bfloat16&amp; a, <span class="keyword">const</span> bfloat16&amp; b) {</div>
<div class="line"><a name="l00287"></a><span class="lineno">  287</span>&#160;  a = bfloat16(<span class="keywordtype">float</span>(a) * <span class="keywordtype">float</span>(b));</div>
<div class="line"><a name="l00288"></a><span class="lineno">  288</span>&#160;  <span class="keywordflow">return</span> a;</div>
<div class="line"><a name="l00289"></a><span class="lineno">  289</span>&#160;}</div>
<div class="line"><a name="l00290"></a><span class="lineno">  290</span>&#160;EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC bfloat16&amp; operator -= (bfloat16&amp; a, <span class="keyword">const</span> bfloat16&amp; b) {</div>
<div class="line"><a name="l00291"></a><span class="lineno">  291</span>&#160;  a = bfloat16(<span class="keywordtype">float</span>(a) - <span class="keywordtype">float</span>(b));</div>
<div class="line"><a name="l00292"></a><span class="lineno">  292</span>&#160;  <span class="keywordflow">return</span> a;</div>
<div class="line"><a name="l00293"></a><span class="lineno">  293</span>&#160;}</div>
<div class="line"><a name="l00294"></a><span class="lineno">  294</span>&#160;EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC bfloat16&amp; operator /= (bfloat16&amp; a, <span class="keyword">const</span> bfloat16&amp; b) {</div>
<div class="line"><a name="l00295"></a><span class="lineno">  295</span>&#160;  a = bfloat16(<span class="keywordtype">float</span>(a) / <span class="keywordtype">float</span>(b));</div>
<div class="line"><a name="l00296"></a><span class="lineno">  296</span>&#160;  <span class="keywordflow">return</span> a;</div>
<div class="line"><a name="l00297"></a><span class="lineno">  297</span>&#160;}</div>
<div class="line"><a name="l00298"></a><span class="lineno">  298</span>&#160;EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC bfloat16 operator++(bfloat16&amp; a) {</div>
<div class="line"><a name="l00299"></a><span class="lineno">  299</span>&#160;  a += bfloat16(1);</div>
<div class="line"><a name="l00300"></a><span class="lineno">  300</span>&#160;  <span class="keywordflow">return</span> a;</div>
<div class="line"><a name="l00301"></a><span class="lineno">  301</span>&#160;}</div>
<div class="line"><a name="l00302"></a><span class="lineno">  302</span>&#160;EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC bfloat16 operator--(bfloat16&amp; a) {</div>
<div class="line"><a name="l00303"></a><span class="lineno">  303</span>&#160;  a -= bfloat16(1);</div>
<div class="line"><a name="l00304"></a><span class="lineno">  304</span>&#160;  <span class="keywordflow">return</span> a;</div>
<div class="line"><a name="l00305"></a><span class="lineno">  305</span>&#160;}</div>
<div class="line"><a name="l00306"></a><span class="lineno">  306</span>&#160;EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC bfloat16 operator++(bfloat16&amp; a, <span class="keywordtype">int</span>) {</div>
<div class="line"><a name="l00307"></a><span class="lineno">  307</span>&#160;  bfloat16 original_value = a;</div>
<div class="line"><a name="l00308"></a><span class="lineno">  308</span>&#160;  ++a;</div>
<div class="line"><a name="l00309"></a><span class="lineno">  309</span>&#160;  <span class="keywordflow">return</span> original_value;</div>
<div class="line"><a name="l00310"></a><span class="lineno">  310</span>&#160;}</div>
<div class="line"><a name="l00311"></a><span class="lineno">  311</span>&#160;EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC bfloat16 operator--(bfloat16&amp; a, <span class="keywordtype">int</span>) {</div>
<div class="line"><a name="l00312"></a><span class="lineno">  312</span>&#160;  bfloat16 original_value = a;</div>
<div class="line"><a name="l00313"></a><span class="lineno">  313</span>&#160;  --a;</div>
<div class="line"><a name="l00314"></a><span class="lineno">  314</span>&#160;  <span class="keywordflow">return</span> original_value;</div>
<div class="line"><a name="l00315"></a><span class="lineno">  315</span>&#160;}</div>
<div class="line"><a name="l00316"></a><span class="lineno">  316</span>&#160;EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC <span class="keywordtype">bool</span> operator == (<span class="keyword">const</span> bfloat16&amp; a, <span class="keyword">const</span> bfloat16&amp; b) {</div>
<div class="line"><a name="l00317"></a><span class="lineno">  317</span>&#160;  <span class="keywordflow">return</span> numext::equal_strict(<span class="keywordtype">float</span>(a),<span class="keywordtype">float</span>(b));</div>
<div class="line"><a name="l00318"></a><span class="lineno">  318</span>&#160;}</div>
<div class="line"><a name="l00319"></a><span class="lineno">  319</span>&#160;EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC <span class="keywordtype">bool</span> operator != (<span class="keyword">const</span> bfloat16&amp; a, <span class="keyword">const</span> bfloat16&amp; b) {</div>
<div class="line"><a name="l00320"></a><span class="lineno">  320</span>&#160;  <span class="keywordflow">return</span> numext::not_equal_strict(<span class="keywordtype">float</span>(a), <span class="keywordtype">float</span>(b));</div>
<div class="line"><a name="l00321"></a><span class="lineno">  321</span>&#160;}</div>
<div class="line"><a name="l00322"></a><span class="lineno">  322</span>&#160;EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC <span class="keywordtype">bool</span> operator &lt; (<span class="keyword">const</span> bfloat16&amp; a, <span class="keyword">const</span> bfloat16&amp; b) {</div>
<div class="line"><a name="l00323"></a><span class="lineno">  323</span>&#160;  <span class="keywordflow">return</span> float(a) &lt; float(b);</div>
<div class="line"><a name="l00324"></a><span class="lineno">  324</span>&#160;}</div>
<div class="line"><a name="l00325"></a><span class="lineno">  325</span>&#160;EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC <span class="keywordtype">bool</span> operator &lt;= (<span class="keyword">const</span> bfloat16&amp; a, <span class="keyword">const</span> bfloat16&amp; b) {</div>
<div class="line"><a name="l00326"></a><span class="lineno">  326</span>&#160;  <span class="keywordflow">return</span> float(a) &lt;= float(b);</div>
<div class="line"><a name="l00327"></a><span class="lineno">  327</span>&#160;}</div>
<div class="line"><a name="l00328"></a><span class="lineno">  328</span>&#160;EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC <span class="keywordtype">bool</span> operator &gt; (<span class="keyword">const</span> bfloat16&amp; a, <span class="keyword">const</span> bfloat16&amp; b) {</div>
<div class="line"><a name="l00329"></a><span class="lineno">  329</span>&#160;  <span class="keywordflow">return</span> float(a) &gt; float(b);</div>
<div class="line"><a name="l00330"></a><span class="lineno">  330</span>&#160;}</div>
<div class="line"><a name="l00331"></a><span class="lineno">  331</span>&#160;EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC <span class="keywordtype">bool</span> operator &gt;= (<span class="keyword">const</span> bfloat16&amp; a, <span class="keyword">const</span> bfloat16&amp; b) {</div>
<div class="line"><a name="l00332"></a><span class="lineno">  332</span>&#160;  <span class="keywordflow">return</span> float(a) &gt;= float(b);</div>
<div class="line"><a name="l00333"></a><span class="lineno">  333</span>&#160;}</div>
<div class="line"><a name="l00334"></a><span class="lineno">  334</span>&#160; </div>
<div class="line"><a name="l00335"></a><span class="lineno">  335</span>&#160;<span class="preprocessor">#if EIGEN_COMP_CLANG &amp;&amp; defined(EIGEN_CUDACC)</span></div>
<div class="line"><a name="l00336"></a><span class="lineno">  336</span>&#160;<span class="preprocessor">#pragma pop_macro(&quot;EIGEN_DEVICE_FUNC&quot;</span>)</div>
<div class="line"><a name="l00337"></a><span class="lineno">  337</span>&#160;<span class="preprocessor">#endif</span></div>
<div class="line"><a name="l00338"></a><span class="lineno">  338</span>&#160;<span class="preprocessor">#endif  </span><span class="comment">// Emulate support for bfloat16 floats</span></div>
<div class="line"><a name="l00339"></a><span class="lineno">  339</span>&#160; </div>
<div class="line"><a name="l00340"></a><span class="lineno">  340</span>&#160;<span class="comment">// Division by an index. Do it in full float precision to avoid accuracy</span></div>
<div class="line"><a name="l00341"></a><span class="lineno">  341</span>&#160;<span class="comment">// issues in converting the denominator to bfloat16.</span></div>
<div class="line"><a name="l00342"></a><span class="lineno">  342</span>&#160;EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC bfloat16 operator / (<span class="keyword">const</span> bfloat16&amp; a, <a class="code" href="namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a> b) {</div>
<div class="line"><a name="l00343"></a><span class="lineno">  343</span>&#160;  <span class="keywordflow">return</span> bfloat16(<span class="keyword">static_cast&lt;</span><span class="keywordtype">float</span><span class="keyword">&gt;</span>(a) / <span class="keyword">static_cast&lt;</span><span class="keywordtype">float</span><span class="keyword">&gt;</span>(b));</div>
<div class="line"><a name="l00344"></a><span class="lineno">  344</span>&#160;}</div>
<div class="line"><a name="l00345"></a><span class="lineno">  345</span>&#160; </div>
<div class="line"><a name="l00346"></a><span class="lineno">  346</span>&#160;EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC __bfloat16_raw truncate_to_bfloat16(<span class="keyword">const</span> <span class="keywordtype">float</span> v) {</div>
<div class="line"><a name="l00347"></a><span class="lineno">  347</span>&#160;<span class="preprocessor">#if defined(EIGEN_USE_HIP_BF16)</span></div>
<div class="line"><a name="l00348"></a><span class="lineno">  348</span>&#160;  <span class="keywordflow">return</span> __bfloat16_raw(__bfloat16_raw::round_to_bfloat16(v, __bfloat16_raw::truncate));</div>
<div class="line"><a name="l00349"></a><span class="lineno">  349</span>&#160;<span class="preprocessor">#else</span></div>
<div class="line"><a name="l00350"></a><span class="lineno">  350</span>&#160;  __bfloat16_raw output;</div>
<div class="line"><a name="l00351"></a><span class="lineno">  351</span>&#160;  <span class="keywordflow">if</span> (numext::isnan EIGEN_NOT_A_MACRO(v)) {</div>
<div class="line"><a name="l00352"></a><span class="lineno">  352</span>&#160;    output.value = std::signbit(v) ? 0xFFC0: 0x7FC0;</div>
<div class="line"><a name="l00353"></a><span class="lineno">  353</span>&#160;    <span class="keywordflow">return</span> output;</div>
<div class="line"><a name="l00354"></a><span class="lineno">  354</span>&#160;  }</div>
<div class="line"><a name="l00355"></a><span class="lineno">  355</span>&#160;  output.value = <span class="keyword">static_cast&lt;</span>numext::uint16_t<span class="keyword">&gt;</span>(numext::bit_cast&lt;numext::uint32_t&gt;(v) &gt;&gt; 16);</div>
<div class="line"><a name="l00356"></a><span class="lineno">  356</span>&#160;  <span class="keywordflow">return</span> output;</div>
<div class="line"><a name="l00357"></a><span class="lineno">  357</span>&#160;<span class="preprocessor">#endif</span></div>
<div class="line"><a name="l00358"></a><span class="lineno">  358</span>&#160;}</div>
<div class="line"><a name="l00359"></a><span class="lineno">  359</span>&#160; </div>
<div class="line"><a name="l00360"></a><span class="lineno">  360</span>&#160;EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR __bfloat16_raw raw_uint16_to_bfloat16(numext::uint16_t value) {</div>
<div class="line"><a name="l00361"></a><span class="lineno">  361</span>&#160;<span class="preprocessor">#if defined(EIGEN_USE_HIP_BF16)</span></div>
<div class="line"><a name="l00362"></a><span class="lineno">  362</span>&#160;  __bfloat16_raw bf;</div>
<div class="line"><a name="l00363"></a><span class="lineno">  363</span>&#160;  bf.data = value;</div>
<div class="line"><a name="l00364"></a><span class="lineno">  364</span>&#160;  <span class="keywordflow">return</span> bf;</div>
<div class="line"><a name="l00365"></a><span class="lineno">  365</span>&#160;<span class="preprocessor">#else</span></div>
<div class="line"><a name="l00366"></a><span class="lineno">  366</span>&#160;  <span class="keywordflow">return</span> __bfloat16_raw(value);</div>
<div class="line"><a name="l00367"></a><span class="lineno">  367</span>&#160;<span class="preprocessor">#endif</span></div>
<div class="line"><a name="l00368"></a><span class="lineno">  368</span>&#160;}</div>
<div class="line"><a name="l00369"></a><span class="lineno">  369</span>&#160; </div>
<div class="line"><a name="l00370"></a><span class="lineno">  370</span>&#160;EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR numext::uint16_t raw_bfloat16_as_uint16(<span class="keyword">const</span> __bfloat16_raw&amp; bf) {</div>
<div class="line"><a name="l00371"></a><span class="lineno">  371</span>&#160;<span class="preprocessor">#if defined(EIGEN_USE_HIP_BF16)</span></div>
<div class="line"><a name="l00372"></a><span class="lineno">  372</span>&#160;  <span class="keywordflow">return</span> bf.data;</div>
<div class="line"><a name="l00373"></a><span class="lineno">  373</span>&#160;<span class="preprocessor">#else</span></div>
<div class="line"><a name="l00374"></a><span class="lineno">  374</span>&#160;  <span class="keywordflow">return</span> bf.value;</div>
<div class="line"><a name="l00375"></a><span class="lineno">  375</span>&#160;<span class="preprocessor">#endif</span></div>
<div class="line"><a name="l00376"></a><span class="lineno">  376</span>&#160;}</div>
<div class="line"><a name="l00377"></a><span class="lineno">  377</span>&#160; </div>
<div class="line"><a name="l00378"></a><span class="lineno">  378</span>&#160;<span class="comment">// float_to_bfloat16_rtne template specialization that does not make any</span></div>
<div class="line"><a name="l00379"></a><span class="lineno">  379</span>&#160;<span class="comment">// assumption about the value of its function argument (ff).</span></div>
<div class="line"><a name="l00380"></a><span class="lineno">  380</span>&#160;<span class="keyword">template</span> &lt;&gt;</div>
<div class="line"><a name="l00381"></a><span class="lineno">  381</span>&#160;EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC __bfloat16_raw float_to_bfloat16_rtne&lt;false&gt;(<span class="keywordtype">float</span> ff) {</div>
<div class="line"><a name="l00382"></a><span class="lineno">  382</span>&#160;<span class="preprocessor">#if defined(EIGEN_USE_HIP_BF16)</span></div>
<div class="line"><a name="l00383"></a><span class="lineno">  383</span>&#160;  <span class="keywordflow">return</span> __bfloat16_raw(__bfloat16_raw::round_to_bfloat16(ff));</div>
<div class="line"><a name="l00384"></a><span class="lineno">  384</span>&#160;<span class="preprocessor">#else</span></div>
<div class="line"><a name="l00385"></a><span class="lineno">  385</span>&#160;  __bfloat16_raw output;</div>
<div class="line"><a name="l00386"></a><span class="lineno">  386</span>&#160; </div>
<div class="line"><a name="l00387"></a><span class="lineno">  387</span>&#160;  <span class="keywordflow">if</span> (numext::isnan EIGEN_NOT_A_MACRO(ff)) {</div>
<div class="line"><a name="l00388"></a><span class="lineno">  388</span>&#160;    <span class="comment">// If the value is a NaN, squash it to a qNaN with msb of fraction set,</span></div>
<div class="line"><a name="l00389"></a><span class="lineno">  389</span>&#160;    <span class="comment">// this makes sure after truncation we don&#39;t end up with an inf.</span></div>
<div class="line"><a name="l00390"></a><span class="lineno">  390</span>&#160;    <span class="comment">//</span></div>
<div class="line"><a name="l00391"></a><span class="lineno">  391</span>&#160;    <span class="comment">// qNaN magic: All exponent bits set + most significant bit of fraction</span></div>
<div class="line"><a name="l00392"></a><span class="lineno">  392</span>&#160;    <span class="comment">// set.</span></div>
<div class="line"><a name="l00393"></a><span class="lineno">  393</span>&#160;    output.value = std::signbit(ff) ? 0xFFC0: 0x7FC0;</div>
<div class="line"><a name="l00394"></a><span class="lineno">  394</span>&#160;  } <span class="keywordflow">else</span> {</div>
<div class="line"><a name="l00395"></a><span class="lineno">  395</span>&#160;    <span class="comment">// Fast rounding algorithm that rounds a half value to nearest even. This</span></div>
<div class="line"><a name="l00396"></a><span class="lineno">  396</span>&#160;    <span class="comment">// reduces expected error when we convert a large number of floats. Here</span></div>
<div class="line"><a name="l00397"></a><span class="lineno">  397</span>&#160;    <span class="comment">// is how it works:</span></div>
<div class="line"><a name="l00398"></a><span class="lineno">  398</span>&#160;    <span class="comment">//</span></div>
<div class="line"><a name="l00399"></a><span class="lineno">  399</span>&#160;    <span class="comment">// Definitions:</span></div>
<div class="line"><a name="l00400"></a><span class="lineno">  400</span>&#160;    <span class="comment">// To convert a float 32 to bfloat16, a float 32 can be viewed as 32 bits</span></div>
<div class="line"><a name="l00401"></a><span class="lineno">  401</span>&#160;    <span class="comment">// with the following tags:</span></div>
<div class="line"><a name="l00402"></a><span class="lineno">  402</span>&#160;    <span class="comment">//</span></div>
<div class="line"><a name="l00403"></a><span class="lineno">  403</span>&#160;    <span class="comment">// Sign |  Exp (8 bits) | Frac (23 bits)</span></div>
<div class="line"><a name="l00404"></a><span class="lineno">  404</span>&#160;    <span class="comment">//  S     EEEEEEEE         FFFFFFLRTTTTTTTTTTTTTTT</span></div>
<div class="line"><a name="l00405"></a><span class="lineno">  405</span>&#160;    <span class="comment">//</span></div>
<div class="line"><a name="l00406"></a><span class="lineno">  406</span>&#160;    <span class="comment">//  S: Sign bit.</span></div>
<div class="line"><a name="l00407"></a><span class="lineno">  407</span>&#160;    <span class="comment">//  E: Exponent bits.</span></div>
<div class="line"><a name="l00408"></a><span class="lineno">  408</span>&#160;    <span class="comment">//  F: First 6 bits of fraction.</span></div>
<div class="line"><a name="l00409"></a><span class="lineno">  409</span>&#160;    <span class="comment">//  L: Least significant bit of resulting bfloat16 if we truncate away the</span></div>
<div class="line"><a name="l00410"></a><span class="lineno">  410</span>&#160;    <span class="comment">//  rest of the float32. This is also the 7th bit of fraction</span></div>
<div class="line"><a name="l00411"></a><span class="lineno">  411</span>&#160;    <span class="comment">//  R: Rounding bit, 8th bit of fraction.</span></div>
<div class="line"><a name="l00412"></a><span class="lineno">  412</span>&#160;    <span class="comment">//  T: Sticky bits, rest of fraction, 15 bits.</span></div>
<div class="line"><a name="l00413"></a><span class="lineno">  413</span>&#160;    <span class="comment">//</span></div>
<div class="line"><a name="l00414"></a><span class="lineno">  414</span>&#160;    <span class="comment">// To round half to nearest even, there are 3 cases where we want to round</span></div>
<div class="line"><a name="l00415"></a><span class="lineno">  415</span>&#160;    <span class="comment">// down (simply truncate the result of the bits away, which consists of</span></div>
<div class="line"><a name="l00416"></a><span class="lineno">  416</span>&#160;    <span class="comment">// rounding bit and sticky bits) and two cases where we want to round up</span></div>
<div class="line"><a name="l00417"></a><span class="lineno">  417</span>&#160;    <span class="comment">// (truncate then add one to the result).</span></div>
<div class="line"><a name="l00418"></a><span class="lineno">  418</span>&#160;    <span class="comment">//</span></div>
<div class="line"><a name="l00419"></a><span class="lineno">  419</span>&#160;    <span class="comment">// The fast converting algorithm simply adds lsb (L) to 0x7fff (15 bits of</span></div>
<div class="line"><a name="l00420"></a><span class="lineno">  420</span>&#160;    <span class="comment">// 1s) as the rounding bias, adds the rounding bias to the input, then</span></div>
<div class="line"><a name="l00421"></a><span class="lineno">  421</span>&#160;    <span class="comment">// truncates the last 16 bits away.</span></div>
<div class="line"><a name="l00422"></a><span class="lineno">  422</span>&#160;    <span class="comment">//</span></div>
<div class="line"><a name="l00423"></a><span class="lineno">  423</span>&#160;    <span class="comment">// To understand how it works, we can analyze this algorithm case by case:</span></div>
<div class="line"><a name="l00424"></a><span class="lineno">  424</span>&#160;    <span class="comment">//</span></div>
<div class="line"><a name="l00425"></a><span class="lineno">  425</span>&#160;    <span class="comment">// 1. L = 0, R = 0:</span></div>
<div class="line"><a name="l00426"></a><span class="lineno">  426</span>&#160;    <span class="comment">//   Expect: round down, this is less than half value.</span></div>
<div class="line"><a name="l00427"></a><span class="lineno">  427</span>&#160;    <span class="comment">//</span></div>
<div class="line"><a name="l00428"></a><span class="lineno">  428</span>&#160;    <span class="comment">//   Algorithm:</span></div>
<div class="line"><a name="l00429"></a><span class="lineno">  429</span>&#160;    <span class="comment">//   - Rounding bias: 0x7fff + 0 = 0x7fff</span></div>
<div class="line"><a name="l00430"></a><span class="lineno">  430</span>&#160;    <span class="comment">//   - Adding rounding bias to input may create any carry, depending on</span></div>
<div class="line"><a name="l00431"></a><span class="lineno">  431</span>&#160;    <span class="comment">//   whether there is any value set to 1 in T bits.</span></div>
<div class="line"><a name="l00432"></a><span class="lineno">  432</span>&#160;    <span class="comment">//   - R may be set to 1 if there is a carry.</span></div>
<div class="line"><a name="l00433"></a><span class="lineno">  433</span>&#160;    <span class="comment">//   - L remains 0.</span></div>
<div class="line"><a name="l00434"></a><span class="lineno">  434</span>&#160;    <span class="comment">//   - Note that this case also handles Inf and -Inf, where all fraction</span></div>
<div class="line"><a name="l00435"></a><span class="lineno">  435</span>&#160;    <span class="comment">//   bits, including L, R and Ts are all 0. The output remains Inf after</span></div>
<div class="line"><a name="l00436"></a><span class="lineno">  436</span>&#160;    <span class="comment">//   this algorithm.</span></div>
<div class="line"><a name="l00437"></a><span class="lineno">  437</span>&#160;    <span class="comment">//</span></div>
<div class="line"><a name="l00438"></a><span class="lineno">  438</span>&#160;    <span class="comment">// 2. L = 1, R = 0:</span></div>
<div class="line"><a name="l00439"></a><span class="lineno">  439</span>&#160;    <span class="comment">//   Expect: round down, this is less than half value.</span></div>
<div class="line"><a name="l00440"></a><span class="lineno">  440</span>&#160;    <span class="comment">//</span></div>
<div class="line"><a name="l00441"></a><span class="lineno">  441</span>&#160;    <span class="comment">//   Algorithm:</span></div>
<div class="line"><a name="l00442"></a><span class="lineno">  442</span>&#160;    <span class="comment">//   - Rounding bias: 0x7fff + 1 = 0x8000</span></div>
<div class="line"><a name="l00443"></a><span class="lineno">  443</span>&#160;    <span class="comment">//   - Adding rounding bias to input doesn&#39;t change sticky bits but</span></div>
<div class="line"><a name="l00444"></a><span class="lineno">  444</span>&#160;    <span class="comment">//   adds 1 to rounding bit.</span></div>
<div class="line"><a name="l00445"></a><span class="lineno">  445</span>&#160;    <span class="comment">//   - L remains 1.</span></div>
<div class="line"><a name="l00446"></a><span class="lineno">  446</span>&#160;    <span class="comment">//</span></div>
<div class="line"><a name="l00447"></a><span class="lineno">  447</span>&#160;    <span class="comment">// 3. L = 0, R = 1, all of T are 0:</span></div>
<div class="line"><a name="l00448"></a><span class="lineno">  448</span>&#160;    <span class="comment">//   Expect: round down, this is exactly at half, the result is already</span></div>
<div class="line"><a name="l00449"></a><span class="lineno">  449</span>&#160;    <span class="comment">//   even (L=0).</span></div>
<div class="line"><a name="l00450"></a><span class="lineno">  450</span>&#160;    <span class="comment">//</span></div>
<div class="line"><a name="l00451"></a><span class="lineno">  451</span>&#160;    <span class="comment">//   Algorithm:</span></div>
<div class="line"><a name="l00452"></a><span class="lineno">  452</span>&#160;    <span class="comment">//   - Rounding bias: 0x7fff + 0 = 0x7fff</span></div>
<div class="line"><a name="l00453"></a><span class="lineno">  453</span>&#160;    <span class="comment">//   - Adding rounding bias to input sets all sticky bits to 1, but</span></div>
<div class="line"><a name="l00454"></a><span class="lineno">  454</span>&#160;    <span class="comment">//   doesn&#39;t create a carry.</span></div>
<div class="line"><a name="l00455"></a><span class="lineno">  455</span>&#160;    <span class="comment">//   - R remains 1.</span></div>
<div class="line"><a name="l00456"></a><span class="lineno">  456</span>&#160;    <span class="comment">//   - L remains 0.</span></div>
<div class="line"><a name="l00457"></a><span class="lineno">  457</span>&#160;    <span class="comment">//</span></div>
<div class="line"><a name="l00458"></a><span class="lineno">  458</span>&#160;    <span class="comment">// 4. L = 1, R = 1:</span></div>
<div class="line"><a name="l00459"></a><span class="lineno">  459</span>&#160;    <span class="comment">//   Expect: round up, this is exactly at half, the result needs to be</span></div>
<div class="line"><a name="l00460"></a><span class="lineno">  460</span>&#160;    <span class="comment">//   round to the next even number.</span></div>
<div class="line"><a name="l00461"></a><span class="lineno">  461</span>&#160;    <span class="comment">//</span></div>
<div class="line"><a name="l00462"></a><span class="lineno">  462</span>&#160;    <span class="comment">//   Algorithm:</span></div>
<div class="line"><a name="l00463"></a><span class="lineno">  463</span>&#160;    <span class="comment">//   - Rounding bias: 0x7fff + 1 = 0x8000</span></div>
<div class="line"><a name="l00464"></a><span class="lineno">  464</span>&#160;    <span class="comment">//   - Adding rounding bias to input doesn&#39;t change sticky bits, but</span></div>
<div class="line"><a name="l00465"></a><span class="lineno">  465</span>&#160;    <span class="comment">//   creates a carry from rounding bit.</span></div>
<div class="line"><a name="l00466"></a><span class="lineno">  466</span>&#160;    <span class="comment">//   - The carry sets L to 0, creates another carry bit and propagate</span></div>
<div class="line"><a name="l00467"></a><span class="lineno">  467</span>&#160;    <span class="comment">//   forward to F bits.</span></div>
<div class="line"><a name="l00468"></a><span class="lineno">  468</span>&#160;    <span class="comment">//   - If all the F bits are 1, a carry then propagates to the exponent</span></div>
<div class="line"><a name="l00469"></a><span class="lineno">  469</span>&#160;    <span class="comment">//   bits, which then creates the minimum value with the next exponent</span></div>
<div class="line"><a name="l00470"></a><span class="lineno">  470</span>&#160;    <span class="comment">//   value. Note that we won&#39;t have the case where exponents are all 1,</span></div>
<div class="line"><a name="l00471"></a><span class="lineno">  471</span>&#160;    <span class="comment">//   since that&#39;s either a NaN (handled in the other if condition) or inf</span></div>
<div class="line"><a name="l00472"></a><span class="lineno">  472</span>&#160;    <span class="comment">//   (handled in case 1).</span></div>
<div class="line"><a name="l00473"></a><span class="lineno">  473</span>&#160;    <span class="comment">//</span></div>
<div class="line"><a name="l00474"></a><span class="lineno">  474</span>&#160;    <span class="comment">// 5. L = 0, R = 1, any of T is 1:</span></div>
<div class="line"><a name="l00475"></a><span class="lineno">  475</span>&#160;    <span class="comment">//   Expect: round up, this is greater than half.</span></div>
<div class="line"><a name="l00476"></a><span class="lineno">  476</span>&#160;    <span class="comment">//</span></div>
<div class="line"><a name="l00477"></a><span class="lineno">  477</span>&#160;    <span class="comment">//   Algorithm:</span></div>
<div class="line"><a name="l00478"></a><span class="lineno">  478</span>&#160;    <span class="comment">//   - Rounding bias: 0x7fff + 0 = 0x7fff</span></div>
<div class="line"><a name="l00479"></a><span class="lineno">  479</span>&#160;    <span class="comment">//   - Adding rounding bias to input creates a carry from sticky bits,</span></div>
<div class="line"><a name="l00480"></a><span class="lineno">  480</span>&#160;    <span class="comment">//   sets rounding bit to 0, then create another carry.</span></div>
<div class="line"><a name="l00481"></a><span class="lineno">  481</span>&#160;    <span class="comment">//   - The second carry sets L to 1.</span></div>
<div class="line"><a name="l00482"></a><span class="lineno">  482</span>&#160;    <span class="comment">//</span></div>
<div class="line"><a name="l00483"></a><span class="lineno">  483</span>&#160;    <span class="comment">// Examples:</span></div>
<div class="line"><a name="l00484"></a><span class="lineno">  484</span>&#160;    <span class="comment">//</span></div>
<div class="line"><a name="l00485"></a><span class="lineno">  485</span>&#160;    <span class="comment">//  Exact half value that is already even:</span></div>
<div class="line"><a name="l00486"></a><span class="lineno">  486</span>&#160;    <span class="comment">//    Input:</span></div>
<div class="line"><a name="l00487"></a><span class="lineno">  487</span>&#160;    <span class="comment">//    Sign |  Exp (8 bit)     | Frac (first 7 bit) | Frac (last 16 bit)</span></div>
<div class="line"><a name="l00488"></a><span class="lineno">  488</span>&#160;    <span class="comment">//     S     E E E E E E E E      F F F F F F L     RTTTTTTTTTTTTTTT</span></div>
<div class="line"><a name="l00489"></a><span class="lineno">  489</span>&#160;    <span class="comment">//     0     0 0 0 0 0 0 0 0      0 0 0 0 0 1 0     1000000000000000</span></div>
<div class="line"><a name="l00490"></a><span class="lineno">  490</span>&#160;    <span class="comment">//</span></div>
<div class="line"><a name="l00491"></a><span class="lineno">  491</span>&#160;    <span class="comment">//     This falls into case 3. We truncate the rest of 16 bits and no</span></div>
<div class="line"><a name="l00492"></a><span class="lineno">  492</span>&#160;    <span class="comment">//     carry is created into F and L:</span></div>
<div class="line"><a name="l00493"></a><span class="lineno">  493</span>&#160;    <span class="comment">//</span></div>
<div class="line"><a name="l00494"></a><span class="lineno">  494</span>&#160;    <span class="comment">//    Output:</span></div>
<div class="line"><a name="l00495"></a><span class="lineno">  495</span>&#160;    <span class="comment">//    Sign |  Exp (8 bit)     | Frac (first 7 bit)</span></div>
<div class="line"><a name="l00496"></a><span class="lineno">  496</span>&#160;    <span class="comment">//     S     E E E E E E E E      F F F F F F L</span></div>
<div class="line"><a name="l00497"></a><span class="lineno">  497</span>&#160;    <span class="comment">//     0     0 0 0 0 0 0 0 0      0 0 0 0 0 1 0</span></div>
<div class="line"><a name="l00498"></a><span class="lineno">  498</span>&#160;    <span class="comment">//</span></div>
<div class="line"><a name="l00499"></a><span class="lineno">  499</span>&#160;    <span class="comment">//  Exact half value, round to next even number:</span></div>
<div class="line"><a name="l00500"></a><span class="lineno">  500</span>&#160;    <span class="comment">//    Input:</span></div>
<div class="line"><a name="l00501"></a><span class="lineno">  501</span>&#160;    <span class="comment">//    Sign |  Exp (8 bit)     | Frac (first 7 bit) | Frac (last 16 bit)</span></div>
<div class="line"><a name="l00502"></a><span class="lineno">  502</span>&#160;    <span class="comment">//     S     E E E E E E E E      F F F F F F L     RTTTTTTTTTTTTTTT</span></div>
<div class="line"><a name="l00503"></a><span class="lineno">  503</span>&#160;    <span class="comment">//     0     0 0 0 0 0 0 0 0      0 0 0 0 0 0 1     1000000000000000</span></div>
<div class="line"><a name="l00504"></a><span class="lineno">  504</span>&#160;    <span class="comment">//</span></div>
<div class="line"><a name="l00505"></a><span class="lineno">  505</span>&#160;    <span class="comment">//     This falls into case 4. We create a carry from R and T,</span></div>
<div class="line"><a name="l00506"></a><span class="lineno">  506</span>&#160;    <span class="comment">//     which then propagates into L and F:</span></div>
<div class="line"><a name="l00507"></a><span class="lineno">  507</span>&#160;    <span class="comment">//</span></div>
<div class="line"><a name="l00508"></a><span class="lineno">  508</span>&#160;    <span class="comment">//    Output:</span></div>
<div class="line"><a name="l00509"></a><span class="lineno">  509</span>&#160;    <span class="comment">//    Sign |  Exp (8 bit)     | Frac (first 7 bit)</span></div>
<div class="line"><a name="l00510"></a><span class="lineno">  510</span>&#160;    <span class="comment">//     S     E E E E E E E E      F F F F F F L</span></div>
<div class="line"><a name="l00511"></a><span class="lineno">  511</span>&#160;    <span class="comment">//     0     0 0 0 0 0 0 0 0      0 0 0 0 0 1 0</span></div>
<div class="line"><a name="l00512"></a><span class="lineno">  512</span>&#160;    <span class="comment">//</span></div>
<div class="line"><a name="l00513"></a><span class="lineno">  513</span>&#160;    <span class="comment">//</span></div>
<div class="line"><a name="l00514"></a><span class="lineno">  514</span>&#160;    <span class="comment">//  Max denormal value round to min normal value:</span></div>
<div class="line"><a name="l00515"></a><span class="lineno">  515</span>&#160;    <span class="comment">//    Input:</span></div>
<div class="line"><a name="l00516"></a><span class="lineno">  516</span>&#160;    <span class="comment">//    Sign |  Exp (8 bit)     | Frac (first 7 bit) | Frac (last 16 bit)</span></div>
<div class="line"><a name="l00517"></a><span class="lineno">  517</span>&#160;    <span class="comment">//     S     E E E E E E E E      F F F F F F L     RTTTTTTTTTTTTTTT</span></div>
<div class="line"><a name="l00518"></a><span class="lineno">  518</span>&#160;    <span class="comment">//     0     0 0 0 0 0 0 0 0      1 1 1 1 1 1 1     1111111111111111</span></div>
<div class="line"><a name="l00519"></a><span class="lineno">  519</span>&#160;    <span class="comment">//</span></div>
<div class="line"><a name="l00520"></a><span class="lineno">  520</span>&#160;    <span class="comment">//     This falls into case 4. We create a carry from R and T,</span></div>
<div class="line"><a name="l00521"></a><span class="lineno">  521</span>&#160;    <span class="comment">//     propagate into L and F, which then propagates into exponent</span></div>
<div class="line"><a name="l00522"></a><span class="lineno">  522</span>&#160;    <span class="comment">//     bits:</span></div>
<div class="line"><a name="l00523"></a><span class="lineno">  523</span>&#160;    <span class="comment">//</span></div>
<div class="line"><a name="l00524"></a><span class="lineno">  524</span>&#160;    <span class="comment">//    Output:</span></div>
<div class="line"><a name="l00525"></a><span class="lineno">  525</span>&#160;    <span class="comment">//    Sign |  Exp (8 bit)     | Frac (first 7 bit)</span></div>
<div class="line"><a name="l00526"></a><span class="lineno">  526</span>&#160;    <span class="comment">//     S     E E E E E E E E      F F F F F F L</span></div>
<div class="line"><a name="l00527"></a><span class="lineno">  527</span>&#160;    <span class="comment">//     0     0 0 0 0 0 0 0 1      0 0 0 0 0 0 0</span></div>
<div class="line"><a name="l00528"></a><span class="lineno">  528</span>&#160;    <span class="comment">//</span></div>
<div class="line"><a name="l00529"></a><span class="lineno">  529</span>&#160;    <span class="comment">//  Max normal value round to Inf:</span></div>
<div class="line"><a name="l00530"></a><span class="lineno">  530</span>&#160;    <span class="comment">//    Input:</span></div>
<div class="line"><a name="l00531"></a><span class="lineno">  531</span>&#160;    <span class="comment">//    Sign |  Exp (8 bit)     | Frac (first 7 bit) | Frac (last 16 bit)</span></div>
<div class="line"><a name="l00532"></a><span class="lineno">  532</span>&#160;    <span class="comment">//     S     E E E E E E E E      F F F F F F L     RTTTTTTTTTTTTTTT</span></div>
<div class="line"><a name="l00533"></a><span class="lineno">  533</span>&#160;    <span class="comment">//     0     1 1 1 1 1 1 1 0      1 1 1 1 1 1 1     1111111111111111</span></div>
<div class="line"><a name="l00534"></a><span class="lineno">  534</span>&#160;    <span class="comment">//</span></div>
<div class="line"><a name="l00535"></a><span class="lineno">  535</span>&#160;    <span class="comment">//     This falls into case 4. We create a carry from R and T,</span></div>
<div class="line"><a name="l00536"></a><span class="lineno">  536</span>&#160;    <span class="comment">//     propagate into L and F, which then propagates into exponent</span></div>
<div class="line"><a name="l00537"></a><span class="lineno">  537</span>&#160;    <span class="comment">//     bits:</span></div>
<div class="line"><a name="l00538"></a><span class="lineno">  538</span>&#160;    <span class="comment">//</span></div>
<div class="line"><a name="l00539"></a><span class="lineno">  539</span>&#160;    <span class="comment">//    Sign |  Exp (8 bit)     | Frac (first 7 bit)</span></div>
<div class="line"><a name="l00540"></a><span class="lineno">  540</span>&#160;    <span class="comment">//     S     E E E E E E E E      F F F F F F L</span></div>
<div class="line"><a name="l00541"></a><span class="lineno">  541</span>&#160;    <span class="comment">//     0     1 1 1 1 1 1 1 1      0 0 0 0 0 0 0</span></div>
<div class="line"><a name="l00542"></a><span class="lineno">  542</span>&#160; </div>
<div class="line"><a name="l00543"></a><span class="lineno">  543</span>&#160;    <span class="comment">// At this point, ff must be either a normal float, or +/-infinity.</span></div>
<div class="line"><a name="l00544"></a><span class="lineno">  544</span>&#160;    output = float_to_bfloat16_rtne&lt;true&gt;(ff);</div>
<div class="line"><a name="l00545"></a><span class="lineno">  545</span>&#160;  }</div>
<div class="line"><a name="l00546"></a><span class="lineno">  546</span>&#160;  <span class="keywordflow">return</span> output;</div>
<div class="line"><a name="l00547"></a><span class="lineno">  547</span>&#160;<span class="preprocessor">#endif</span></div>
<div class="line"><a name="l00548"></a><span class="lineno">  548</span>&#160;}</div>
<div class="line"><a name="l00549"></a><span class="lineno">  549</span>&#160; </div>
<div class="line"><a name="l00550"></a><span class="lineno">  550</span>&#160;<span class="comment">// float_to_bfloat16_rtne template specialization that assumes that its function</span></div>
<div class="line"><a name="l00551"></a><span class="lineno">  551</span>&#160;<span class="comment">// argument (ff) is either a normal floating point number, or +/-infinity, or</span></div>
<div class="line"><a name="l00552"></a><span class="lineno">  552</span>&#160;<span class="comment">// zero. Used to improve the runtime performance of conversion from an integer</span></div>
<div class="line"><a name="l00553"></a><span class="lineno">  553</span>&#160;<span class="comment">// type to bfloat16.</span></div>
<div class="line"><a name="l00554"></a><span class="lineno">  554</span>&#160;<span class="keyword">template</span> &lt;&gt;</div>
<div class="line"><a name="l00555"></a><span class="lineno">  555</span>&#160;EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC __bfloat16_raw float_to_bfloat16_rtne&lt;true&gt;(<span class="keywordtype">float</span> ff) {</div>
<div class="line"><a name="l00556"></a><span class="lineno">  556</span>&#160;<span class="preprocessor">#if defined(EIGEN_USE_HIP_BF16)</span></div>
<div class="line"><a name="l00557"></a><span class="lineno">  557</span>&#160;    <span class="keywordflow">return</span> __bfloat16_raw(__bfloat16_raw::round_to_bfloat16(ff));</div>
<div class="line"><a name="l00558"></a><span class="lineno">  558</span>&#160;<span class="preprocessor">#else</span></div>
<div class="line"><a name="l00559"></a><span class="lineno">  559</span>&#160;    numext::uint32_t input = numext::bit_cast&lt;numext::uint32_t&gt;(ff);</div>
<div class="line"><a name="l00560"></a><span class="lineno">  560</span>&#160;    __bfloat16_raw output;</div>
<div class="line"><a name="l00561"></a><span class="lineno">  561</span>&#160; </div>
<div class="line"><a name="l00562"></a><span class="lineno">  562</span>&#160;    <span class="comment">// Least significant bit of resulting bfloat.</span></div>
<div class="line"><a name="l00563"></a><span class="lineno">  563</span>&#160;    numext::uint32_t lsb = (input &gt;&gt; 16) &amp; 1;</div>
<div class="line"><a name="l00564"></a><span class="lineno">  564</span>&#160;    numext::uint32_t rounding_bias = 0x7fff + lsb;</div>
<div class="line"><a name="l00565"></a><span class="lineno">  565</span>&#160;    input += rounding_bias;</div>
<div class="line"><a name="l00566"></a><span class="lineno">  566</span>&#160;    output.value = <span class="keyword">static_cast&lt;</span>numext::uint16_t<span class="keyword">&gt;</span>(input &gt;&gt; 16);</div>
<div class="line"><a name="l00567"></a><span class="lineno">  567</span>&#160;    <span class="keywordflow">return</span> output;</div>
<div class="line"><a name="l00568"></a><span class="lineno">  568</span>&#160;<span class="preprocessor">#endif</span></div>
<div class="line"><a name="l00569"></a><span class="lineno">  569</span>&#160;}</div>
<div class="line"><a name="l00570"></a><span class="lineno">  570</span>&#160; </div>
<div class="line"><a name="l00571"></a><span class="lineno">  571</span>&#160;EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC <span class="keywordtype">float</span> bfloat16_to_float(__bfloat16_raw h) {</div>
<div class="line"><a name="l00572"></a><span class="lineno">  572</span>&#160;<span class="preprocessor">#if defined(EIGEN_USE_HIP_BF16)</span></div>
<div class="line"><a name="l00573"></a><span class="lineno">  573</span>&#160;    <span class="keywordflow">return</span> <span class="keyword">static_cast&lt;</span><span class="keywordtype">float</span><span class="keyword">&gt;</span>(h);</div>
<div class="line"><a name="l00574"></a><span class="lineno">  574</span>&#160;<span class="preprocessor">#else</span></div>
<div class="line"><a name="l00575"></a><span class="lineno">  575</span>&#160;    <span class="keywordflow">return</span> numext::bit_cast&lt;float&gt;(<span class="keyword">static_cast&lt;</span>numext::uint32_t<span class="keyword">&gt;</span>(h.value) &lt;&lt; 16);</div>
<div class="line"><a name="l00576"></a><span class="lineno">  576</span>&#160;<span class="preprocessor">#endif</span></div>
<div class="line"><a name="l00577"></a><span class="lineno">  577</span>&#160;}</div>
<div class="line"><a name="l00578"></a><span class="lineno">  578</span>&#160; </div>
<div class="line"><a name="l00579"></a><span class="lineno">  579</span>&#160;<span class="comment">// --- standard functions ---</span></div>
<div class="line"><a name="l00580"></a><span class="lineno">  580</span>&#160; </div>
<div class="line"><a name="l00581"></a><span class="lineno">  581</span>&#160;EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC bool (<a class="code" href="namespaceEigen.html#a1f1103712e337c4c96a05f949637a4c8">isinf</a>)(<span class="keyword">const</span> bfloat16&amp; a) {</div>
<div class="line"><a name="l00582"></a><span class="lineno">  582</span>&#160;  EIGEN_USING_STD(<a class="code" href="namespaceEigen.html#a1f1103712e337c4c96a05f949637a4c8">isinf</a>);</div>
<div class="line"><a name="l00583"></a><span class="lineno">  583</span>&#160;<span class="preprocessor">#if defined(EIGEN_USE_HIP_BF16)</span></div>
<div class="line"><a name="l00584"></a><span class="lineno">  584</span>&#160;  <span class="keywordflow">return</span> (<a class="code" href="namespaceEigen.html#a1f1103712e337c4c96a05f949637a4c8">isinf</a>)(a); <span class="comment">// Uses HIP hip_bfloat16 isinf operator</span></div>
<div class="line"><a name="l00585"></a><span class="lineno">  585</span>&#160;<span class="preprocessor">#else</span></div>
<div class="line"><a name="l00586"></a><span class="lineno">  586</span>&#160;  <span class="keywordflow">return</span> (<a class="code" href="namespaceEigen.html#a1f1103712e337c4c96a05f949637a4c8">isinf</a>)(float(a));</div>
<div class="line"><a name="l00587"></a><span class="lineno">  587</span>&#160;<span class="preprocessor">#endif</span></div>
<div class="line"><a name="l00588"></a><span class="lineno">  588</span>&#160;}</div>
<div class="line"><a name="l00589"></a><span class="lineno">  589</span>&#160;EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC bool (<a class="code" href="namespaceEigen.html#a99adfc5178f3fd5488304284388b2a10">isnan</a>)(<span class="keyword">const</span> bfloat16&amp; a) {</div>
<div class="line"><a name="l00590"></a><span class="lineno">  590</span>&#160;  EIGEN_USING_STD(<a class="code" href="namespaceEigen.html#a99adfc5178f3fd5488304284388b2a10">isnan</a>);</div>
<div class="line"><a name="l00591"></a><span class="lineno">  591</span>&#160;<span class="preprocessor">#if defined(EIGEN_USE_HIP_BF16)</span></div>
<div class="line"><a name="l00592"></a><span class="lineno">  592</span>&#160;  <span class="keywordflow">return</span> (<a class="code" href="namespaceEigen.html#a99adfc5178f3fd5488304284388b2a10">isnan</a>)(a); <span class="comment">// Uses HIP hip_bfloat16 isnan operator</span></div>
<div class="line"><a name="l00593"></a><span class="lineno">  593</span>&#160;<span class="preprocessor">#else</span></div>
<div class="line"><a name="l00594"></a><span class="lineno">  594</span>&#160;  <span class="keywordflow">return</span> (<a class="code" href="namespaceEigen.html#a99adfc5178f3fd5488304284388b2a10">isnan</a>)(float(a));</div>
<div class="line"><a name="l00595"></a><span class="lineno">  595</span>&#160;<span class="preprocessor">#endif</span></div>
<div class="line"><a name="l00596"></a><span class="lineno">  596</span>&#160;}</div>
<div class="line"><a name="l00597"></a><span class="lineno">  597</span>&#160;EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC bool (<a class="code" href="namespaceEigen.html#aba24ec81dec745a00b7f33adead89811">isfinite</a>)(<span class="keyword">const</span> bfloat16&amp; a) {</div>
<div class="line"><a name="l00598"></a><span class="lineno">  598</span>&#160;  <span class="keywordflow">return</span> !(<a class="code" href="namespaceEigen.html#a1f1103712e337c4c96a05f949637a4c8">isinf</a> EIGEN_NOT_A_MACRO (a)) &amp;&amp; !(<a class="code" href="namespaceEigen.html#a99adfc5178f3fd5488304284388b2a10">isnan</a> EIGEN_NOT_A_MACRO (a));</div>
<div class="line"><a name="l00599"></a><span class="lineno">  599</span>&#160;}</div>
<div class="line"><a name="l00600"></a><span class="lineno">  600</span>&#160; </div>
<div class="line"><a name="l00601"></a><span class="lineno">  601</span>&#160;EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC bfloat16 <a class="code" href="namespaceEigen.html#ae27242789e7e62a8c42579b79be59b1a">abs</a>(<span class="keyword">const</span> bfloat16&amp; a) {</div>
<div class="line"><a name="l00602"></a><span class="lineno">  602</span>&#160;  numext::uint16_t x = numext::bit_cast&lt;numext::uint16_t&gt;(a) &amp; 0x7FFF;</div>
<div class="line"><a name="l00603"></a><span class="lineno">  603</span>&#160;  <span class="keywordflow">return</span> numext::bit_cast&lt;bfloat16&gt;(x);</div>
<div class="line"><a name="l00604"></a><span class="lineno">  604</span>&#160;}</div>
<div class="line"><a name="l00605"></a><span class="lineno">  605</span>&#160;EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC bfloat16 <a class="code" href="namespaceEigen.html#ae491aecf7dab66ac7e11008c5766694d">exp</a>(<span class="keyword">const</span> bfloat16&amp; a) {</div>
<div class="line"><a name="l00606"></a><span class="lineno">  606</span>&#160;  <span class="keywordflow">return</span> bfloat16(::expf(<span class="keywordtype">float</span>(a)));</div>
<div class="line"><a name="l00607"></a><span class="lineno">  607</span>&#160;}</div>
<div class="line"><a name="l00608"></a><span class="lineno">  608</span>&#160;EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC bfloat16 <a class="code" href="namespaceEigen.html#ae7cb2544e4e745bc0067fe793e3f2f81">expm1</a>(<span class="keyword">const</span> bfloat16&amp; a) {</div>
<div class="line"><a name="l00609"></a><span class="lineno">  609</span>&#160;  <span class="keywordflow">return</span> bfloat16(numext::expm1(<span class="keywordtype">float</span>(a)));</div>
<div class="line"><a name="l00610"></a><span class="lineno">  610</span>&#160;}</div>
<div class="line"><a name="l00611"></a><span class="lineno">  611</span>&#160;EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC bfloat16 <a class="code" href="namespaceEigen.html#ae8bb75ba4f5f30a7571146dbfa653c6d">log</a>(<span class="keyword">const</span> bfloat16&amp; a) {</div>
<div class="line"><a name="l00612"></a><span class="lineno">  612</span>&#160;  <span class="keywordflow">return</span> bfloat16(::logf(<span class="keywordtype">float</span>(a)));</div>
<div class="line"><a name="l00613"></a><span class="lineno">  613</span>&#160;}</div>
<div class="line"><a name="l00614"></a><span class="lineno">  614</span>&#160;EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC bfloat16 <a class="code" href="namespaceEigen.html#ac5c8a2cded6b59628f2de04f24d2fff4">log1p</a>(<span class="keyword">const</span> bfloat16&amp; a) {</div>
<div class="line"><a name="l00615"></a><span class="lineno">  615</span>&#160;  <span class="keywordflow">return</span> bfloat16(numext::log1p(<span class="keywordtype">float</span>(a)));</div>
<div class="line"><a name="l00616"></a><span class="lineno">  616</span>&#160;}</div>
<div class="line"><a name="l00617"></a><span class="lineno">  617</span>&#160;EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC bfloat16 <a class="code" href="namespaceEigen.html#a25256faeec3ffd0f3615a0e1e45dfb14">log10</a>(<span class="keyword">const</span> bfloat16&amp; a) {</div>
<div class="line"><a name="l00618"></a><span class="lineno">  618</span>&#160;  <span class="keywordflow">return</span> bfloat16(::log10f(<span class="keywordtype">float</span>(a)));</div>
<div class="line"><a name="l00619"></a><span class="lineno">  619</span>&#160;}</div>
<div class="line"><a name="l00620"></a><span class="lineno">  620</span>&#160;EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC bfloat16 <a class="code" href="namespaceEigen.html#ad2d0241ffaaa3b0b04ec70b59ab066d4">log2</a>(<span class="keyword">const</span> bfloat16&amp; a) {</div>
<div class="line"><a name="l00621"></a><span class="lineno">  621</span>&#160;  <span class="keywordflow">return</span> bfloat16(<span class="keyword">static_cast&lt;</span><span class="keywordtype">float</span><span class="keyword">&gt;</span>(EIGEN_LOG2E) * ::logf(<span class="keywordtype">float</span>(a)));</div>
<div class="line"><a name="l00622"></a><span class="lineno">  622</span>&#160;}</div>
<div class="line"><a name="l00623"></a><span class="lineno">  623</span>&#160;EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC bfloat16 <a class="code" href="namespaceEigen.html#af4f536e8ea56702e63088efb3706d1f0">sqrt</a>(<span class="keyword">const</span> bfloat16&amp; a) {</div>
<div class="line"><a name="l00624"></a><span class="lineno">  624</span>&#160;  <span class="keywordflow">return</span> bfloat16(::sqrtf(<span class="keywordtype">float</span>(a)));</div>
<div class="line"><a name="l00625"></a><span class="lineno">  625</span>&#160;}</div>
<div class="line"><a name="l00626"></a><span class="lineno">  626</span>&#160;EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC bfloat16 pow(<span class="keyword">const</span> bfloat16&amp; a, <span class="keyword">const</span> bfloat16&amp; b) {</div>
<div class="line"><a name="l00627"></a><span class="lineno">  627</span>&#160;  <span class="keywordflow">return</span> bfloat16(::powf(<span class="keywordtype">float</span>(a), <span class="keywordtype">float</span>(b)));</div>
<div class="line"><a name="l00628"></a><span class="lineno">  628</span>&#160;}</div>
<div class="line"><a name="l00629"></a><span class="lineno">  629</span>&#160;EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC bfloat16 <a class="code" href="namespaceEigen.html#ae6e8ad270ff41c088d7651567594f796">sin</a>(<span class="keyword">const</span> bfloat16&amp; a) {</div>
<div class="line"><a name="l00630"></a><span class="lineno">  630</span>&#160;  <span class="keywordflow">return</span> bfloat16(::sinf(<span class="keywordtype">float</span>(a)));</div>
<div class="line"><a name="l00631"></a><span class="lineno">  631</span>&#160;}</div>
<div class="line"><a name="l00632"></a><span class="lineno">  632</span>&#160;EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC bfloat16 <a class="code" href="namespaceEigen.html#ad01d50a42869218f1d54af13f71517a6">cos</a>(<span class="keyword">const</span> bfloat16&amp; a) {</div>
<div class="line"><a name="l00633"></a><span class="lineno">  633</span>&#160;  <span class="keywordflow">return</span> bfloat16(::cosf(<span class="keywordtype">float</span>(a)));</div>
<div class="line"><a name="l00634"></a><span class="lineno">  634</span>&#160;}</div>
<div class="line"><a name="l00635"></a><span class="lineno">  635</span>&#160;EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC bfloat16 <a class="code" href="namespaceEigen.html#a3bc116a6243f38c22f851581aa7b521a">tan</a>(<span class="keyword">const</span> bfloat16&amp; a) {</div>
<div class="line"><a name="l00636"></a><span class="lineno">  636</span>&#160;  <span class="keywordflow">return</span> bfloat16(::tanf(<span class="keywordtype">float</span>(a)));</div>
<div class="line"><a name="l00637"></a><span class="lineno">  637</span>&#160;}</div>
<div class="line"><a name="l00638"></a><span class="lineno">  638</span>&#160;EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC bfloat16 <a class="code" href="namespaceEigen.html#a6c5c246b877ac331495d21e7a5d51616">asin</a>(<span class="keyword">const</span> bfloat16&amp; a) {</div>
<div class="line"><a name="l00639"></a><span class="lineno">  639</span>&#160;  <span class="keywordflow">return</span> bfloat16(::asinf(<span class="keywordtype">float</span>(a)));</div>
<div class="line"><a name="l00640"></a><span class="lineno">  640</span>&#160;}</div>
<div class="line"><a name="l00641"></a><span class="lineno">  641</span>&#160;EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC bfloat16 <a class="code" href="namespaceEigen.html#a3fe3a136370fefae062591304c6a7ebd">acos</a>(<span class="keyword">const</span> bfloat16&amp; a) {</div>
<div class="line"><a name="l00642"></a><span class="lineno">  642</span>&#160;  <span class="keywordflow">return</span> bfloat16(::acosf(<span class="keywordtype">float</span>(a)));</div>
<div class="line"><a name="l00643"></a><span class="lineno">  643</span>&#160;}</div>
<div class="line"><a name="l00644"></a><span class="lineno">  644</span>&#160;EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC bfloat16 <a class="code" href="namespaceEigen.html#a230744e17147d12e8ef3f2fc3796f64f">atan</a>(<span class="keyword">const</span> bfloat16&amp; a) {</div>
<div class="line"><a name="l00645"></a><span class="lineno">  645</span>&#160;  <span class="keywordflow">return</span> bfloat16(::atanf(<span class="keywordtype">float</span>(a)));</div>
<div class="line"><a name="l00646"></a><span class="lineno">  646</span>&#160;}</div>
<div class="line"><a name="l00647"></a><span class="lineno">  647</span>&#160;EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC bfloat16 <a class="code" href="namespaceEigen.html#af284ce359b6efd4b594a9f8a1f5e5d96">sinh</a>(<span class="keyword">const</span> bfloat16&amp; a) {</div>
<div class="line"><a name="l00648"></a><span class="lineno">  648</span>&#160;  <span class="keywordflow">return</span> bfloat16(::sinhf(<span class="keywordtype">float</span>(a)));</div>
<div class="line"><a name="l00649"></a><span class="lineno">  649</span>&#160;}</div>
<div class="line"><a name="l00650"></a><span class="lineno">  650</span>&#160;EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC bfloat16 <a class="code" href="namespaceEigen.html#a34b99a26a2a1e7ff985a5ace16eedfcb">cosh</a>(<span class="keyword">const</span> bfloat16&amp; a) {</div>
<div class="line"><a name="l00651"></a><span class="lineno">  651</span>&#160;  <span class="keywordflow">return</span> bfloat16(::coshf(<span class="keywordtype">float</span>(a)));</div>
<div class="line"><a name="l00652"></a><span class="lineno">  652</span>&#160;}</div>
<div class="line"><a name="l00653"></a><span class="lineno">  653</span>&#160;EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC bfloat16 <a class="code" href="namespaceEigen.html#a0110c233d357169fd58fdf5656992a98">tanh</a>(<span class="keyword">const</span> bfloat16&amp; a) {</div>
<div class="line"><a name="l00654"></a><span class="lineno">  654</span>&#160;  <span class="keywordflow">return</span> bfloat16(::tanhf(<span class="keywordtype">float</span>(a)));</div>
<div class="line"><a name="l00655"></a><span class="lineno">  655</span>&#160;}</div>
<div class="line"><a name="l00656"></a><span class="lineno">  656</span>&#160;<span class="preprocessor">#if EIGEN_HAS_CXX11_MATH</span></div>
<div class="line"><a name="l00657"></a><span class="lineno">  657</span>&#160;EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC bfloat16 <a class="code" href="namespaceEigen.html#a727dd851cc82a62574145bc5abdc7aed">asinh</a>(<span class="keyword">const</span> bfloat16&amp; a) {</div>
<div class="line"><a name="l00658"></a><span class="lineno">  658</span>&#160;  <span class="keywordflow">return</span> bfloat16(::asinhf(<span class="keywordtype">float</span>(a)));</div>
<div class="line"><a name="l00659"></a><span class="lineno">  659</span>&#160;}</div>
<div class="line"><a name="l00660"></a><span class="lineno">  660</span>&#160;EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC bfloat16 <a class="code" href="namespaceEigen.html#a97676fabe9a7466cc2ccb6a2d0f83471">acosh</a>(<span class="keyword">const</span> bfloat16&amp; a) {</div>
<div class="line"><a name="l00661"></a><span class="lineno">  661</span>&#160;  <span class="keywordflow">return</span> bfloat16(::acoshf(<span class="keywordtype">float</span>(a)));</div>
<div class="line"><a name="l00662"></a><span class="lineno">  662</span>&#160;}</div>
<div class="line"><a name="l00663"></a><span class="lineno">  663</span>&#160;EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC bfloat16 <a class="code" href="namespaceEigen.html#a45d37a9f1c784eb8ab61ed24f07f436f">atanh</a>(<span class="keyword">const</span> bfloat16&amp; a) {</div>
<div class="line"><a name="l00664"></a><span class="lineno">  664</span>&#160;  <span class="keywordflow">return</span> bfloat16(::atanhf(<span class="keywordtype">float</span>(a)));</div>
<div class="line"><a name="l00665"></a><span class="lineno">  665</span>&#160;}</div>
<div class="line"><a name="l00666"></a><span class="lineno">  666</span>&#160;<span class="preprocessor">#endif</span></div>
<div class="line"><a name="l00667"></a><span class="lineno">  667</span>&#160;EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC bfloat16 <a class="code" href="namespaceEigen.html#abf03d773a87830bc7fde51bcd94c89a0">floor</a>(<span class="keyword">const</span> bfloat16&amp; a) {</div>
<div class="line"><a name="l00668"></a><span class="lineno">  668</span>&#160;  <span class="keywordflow">return</span> bfloat16(::floorf(<span class="keywordtype">float</span>(a)));</div>
<div class="line"><a name="l00669"></a><span class="lineno">  669</span>&#160;}</div>
<div class="line"><a name="l00670"></a><span class="lineno">  670</span>&#160;EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC bfloat16 <a class="code" href="namespaceEigen.html#aa73e38be0689a463ae14141b9cf89c35">ceil</a>(<span class="keyword">const</span> bfloat16&amp; a) {</div>
<div class="line"><a name="l00671"></a><span class="lineno">  671</span>&#160;  <span class="keywordflow">return</span> bfloat16(::ceilf(<span class="keywordtype">float</span>(a)));</div>
<div class="line"><a name="l00672"></a><span class="lineno">  672</span>&#160;}</div>
<div class="line"><a name="l00673"></a><span class="lineno">  673</span>&#160;EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC bfloat16 <a class="code" href="namespaceEigen.html#a0211fe61b9e390dfd8ca213fe9c7fca3">rint</a>(<span class="keyword">const</span> bfloat16&amp; a) {</div>
<div class="line"><a name="l00674"></a><span class="lineno">  674</span>&#160;  <span class="keywordflow">return</span> bfloat16(::rintf(<span class="keywordtype">float</span>(a)));</div>
<div class="line"><a name="l00675"></a><span class="lineno">  675</span>&#160;}</div>
<div class="line"><a name="l00676"></a><span class="lineno">  676</span>&#160;EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC bfloat16 <a class="code" href="namespaceEigen.html#ad9eaa98e8016ef17024a18a2f3e5bef3">round</a>(<span class="keyword">const</span> bfloat16&amp; a) {</div>
<div class="line"><a name="l00677"></a><span class="lineno">  677</span>&#160;  <span class="keywordflow">return</span> bfloat16(::roundf(<span class="keywordtype">float</span>(a)));</div>
<div class="line"><a name="l00678"></a><span class="lineno">  678</span>&#160;}</div>
<div class="line"><a name="l00679"></a><span class="lineno">  679</span>&#160;EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC bfloat16 fmod(<span class="keyword">const</span> bfloat16&amp; a, <span class="keyword">const</span> bfloat16&amp; b) {</div>
<div class="line"><a name="l00680"></a><span class="lineno">  680</span>&#160;  <span class="keywordflow">return</span> bfloat16(::fmodf(<span class="keywordtype">float</span>(a), <span class="keywordtype">float</span>(b)));</div>
<div class="line"><a name="l00681"></a><span class="lineno">  681</span>&#160;}</div>
<div class="line"><a name="l00682"></a><span class="lineno">  682</span>&#160; </div>
<div class="line"><a name="l00683"></a><span class="lineno">  683</span>&#160;EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC bfloat16 (min)(<span class="keyword">const</span> bfloat16&amp; a, <span class="keyword">const</span> bfloat16&amp; b) {</div>
<div class="line"><a name="l00684"></a><span class="lineno">  684</span>&#160;  <span class="keyword">const</span> <span class="keywordtype">float</span> f1 = <span class="keyword">static_cast&lt;</span><span class="keywordtype">float</span><span class="keyword">&gt;</span>(a);</div>
<div class="line"><a name="l00685"></a><span class="lineno">  685</span>&#160;  <span class="keyword">const</span> <span class="keywordtype">float</span> f2 = <span class="keyword">static_cast&lt;</span><span class="keywordtype">float</span><span class="keyword">&gt;</span>(b);</div>
<div class="line"><a name="l00686"></a><span class="lineno">  686</span>&#160;  <span class="keywordflow">return</span> f2 &lt; f1 ? b : a;</div>
<div class="line"><a name="l00687"></a><span class="lineno">  687</span>&#160;}</div>
<div class="line"><a name="l00688"></a><span class="lineno">  688</span>&#160; </div>
<div class="line"><a name="l00689"></a><span class="lineno">  689</span>&#160;EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC bfloat16 (max)(<span class="keyword">const</span> bfloat16&amp; a, <span class="keyword">const</span> bfloat16&amp; b) {</div>
<div class="line"><a name="l00690"></a><span class="lineno">  690</span>&#160;  <span class="keyword">const</span> <span class="keywordtype">float</span> f1 = <span class="keyword">static_cast&lt;</span><span class="keywordtype">float</span><span class="keyword">&gt;</span>(a);</div>
<div class="line"><a name="l00691"></a><span class="lineno">  691</span>&#160;  <span class="keyword">const</span> <span class="keywordtype">float</span> f2 = <span class="keyword">static_cast&lt;</span><span class="keywordtype">float</span><span class="keyword">&gt;</span>(b);</div>
<div class="line"><a name="l00692"></a><span class="lineno">  692</span>&#160;  <span class="keywordflow">return</span> f1 &lt; f2 ? b : a;</div>
<div class="line"><a name="l00693"></a><span class="lineno">  693</span>&#160;}</div>
<div class="line"><a name="l00694"></a><span class="lineno">  694</span>&#160; </div>
<div class="line"><a name="l00695"></a><span class="lineno">  695</span>&#160;EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC bfloat16 fmin(<span class="keyword">const</span> bfloat16&amp; a, <span class="keyword">const</span> bfloat16&amp; b) {</div>
<div class="line"><a name="l00696"></a><span class="lineno">  696</span>&#160;  <span class="keyword">const</span> <span class="keywordtype">float</span> f1 = <span class="keyword">static_cast&lt;</span><span class="keywordtype">float</span><span class="keyword">&gt;</span>(a);</div>
<div class="line"><a name="l00697"></a><span class="lineno">  697</span>&#160;  <span class="keyword">const</span> <span class="keywordtype">float</span> f2 = <span class="keyword">static_cast&lt;</span><span class="keywordtype">float</span><span class="keyword">&gt;</span>(b);</div>
<div class="line"><a name="l00698"></a><span class="lineno">  698</span>&#160;  <span class="keywordflow">return</span> bfloat16(::fminf(f1, f2));</div>
<div class="line"><a name="l00699"></a><span class="lineno">  699</span>&#160;}</div>
<div class="line"><a name="l00700"></a><span class="lineno">  700</span>&#160; </div>
<div class="line"><a name="l00701"></a><span class="lineno">  701</span>&#160;EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC bfloat16 fmax(<span class="keyword">const</span> bfloat16&amp; a, <span class="keyword">const</span> bfloat16&amp; b) {</div>
<div class="line"><a name="l00702"></a><span class="lineno">  702</span>&#160;  <span class="keyword">const</span> <span class="keywordtype">float</span> f1 = <span class="keyword">static_cast&lt;</span><span class="keywordtype">float</span><span class="keyword">&gt;</span>(a);</div>
<div class="line"><a name="l00703"></a><span class="lineno">  703</span>&#160;  <span class="keyword">const</span> <span class="keywordtype">float</span> f2 = <span class="keyword">static_cast&lt;</span><span class="keywordtype">float</span><span class="keyword">&gt;</span>(b);</div>
<div class="line"><a name="l00704"></a><span class="lineno">  704</span>&#160;  <span class="keywordflow">return</span> bfloat16(::fmaxf(f1, f2));</div>
<div class="line"><a name="l00705"></a><span class="lineno">  705</span>&#160;}</div>
<div class="line"><a name="l00706"></a><span class="lineno">  706</span>&#160; </div>
<div class="line"><a name="l00707"></a><span class="lineno">  707</span>&#160;<span class="preprocessor">#ifndef EIGEN_NO_IO</span></div>
<div class="line"><a name="l00708"></a><span class="lineno">  708</span>&#160;EIGEN_ALWAYS_INLINE std::ostream&amp; operator &lt;&lt; (std::ostream&amp; os, <span class="keyword">const</span> bfloat16&amp; v) {</div>
<div class="line"><a name="l00709"></a><span class="lineno">  709</span>&#160;  os &lt;&lt; static_cast&lt;float&gt;(v);</div>
<div class="line"><a name="l00710"></a><span class="lineno">  710</span>&#160;  <span class="keywordflow">return</span> os;</div>
<div class="line"><a name="l00711"></a><span class="lineno">  711</span>&#160;}</div>
<div class="line"><a name="l00712"></a><span class="lineno">  712</span>&#160;<span class="preprocessor">#endif</span></div>
<div class="line"><a name="l00713"></a><span class="lineno">  713</span>&#160; </div>
<div class="line"><a name="l00714"></a><span class="lineno">  714</span>&#160;} <span class="comment">// namespace bfloat16_impl</span></div>
<div class="line"><a name="l00715"></a><span class="lineno">  715</span>&#160; </div>
<div class="line"><a name="l00716"></a><span class="lineno">  716</span>&#160;<span class="keyword">namespace </span>internal {</div>
<div class="line"><a name="l00717"></a><span class="lineno">  717</span>&#160; </div>
<div class="line"><a name="l00718"></a><span class="lineno">  718</span>&#160;<span class="keyword">template</span>&lt;&gt;</div>
<div class="line"><a name="l00719"></a><span class="lineno">  719</span>&#160;<span class="keyword">struct </span>random_default_impl&lt;bfloat16, false, false&gt;</div>
<div class="line"><a name="l00720"></a><span class="lineno">  720</span>&#160;{</div>
<div class="line"><a name="l00721"></a><span class="lineno">  721</span>&#160;  <span class="keyword">static</span> <span class="keyword">inline</span> bfloat16 run(<span class="keyword">const</span> bfloat16&amp; x, <span class="keyword">const</span> bfloat16&amp; y)</div>
<div class="line"><a name="l00722"></a><span class="lineno">  722</span>&#160;  {</div>
<div class="line"><a name="l00723"></a><span class="lineno">  723</span>&#160;    <span class="keywordflow">return</span> x + (y-x) * bfloat16(<span class="keywordtype">float</span>(std::rand()) / float(RAND_MAX));</div>
<div class="line"><a name="l00724"></a><span class="lineno">  724</span>&#160;  }</div>
<div class="line"><a name="l00725"></a><span class="lineno">  725</span>&#160;  <span class="keyword">static</span> <span class="keyword">inline</span> bfloat16 run()</div>
<div class="line"><a name="l00726"></a><span class="lineno">  726</span>&#160;  {</div>
<div class="line"><a name="l00727"></a><span class="lineno">  727</span>&#160;    <span class="keywordflow">return</span> run(bfloat16(-1.f), bfloat16(1.f));</div>
<div class="line"><a name="l00728"></a><span class="lineno">  728</span>&#160;  }</div>
<div class="line"><a name="l00729"></a><span class="lineno">  729</span>&#160;};</div>
<div class="line"><a name="l00730"></a><span class="lineno">  730</span>&#160; </div>
<div class="line"><a name="l00731"></a><span class="lineno">  731</span>&#160;<span class="keyword">template</span>&lt;&gt; <span class="keyword">struct </span>is_arithmetic&lt;bfloat16&gt; { <span class="keyword">enum</span> { value = <span class="keyword">true</span> }; };</div>
<div class="line"><a name="l00732"></a><span class="lineno">  732</span>&#160; </div>
<div class="line"><a name="l00733"></a><span class="lineno">  733</span>&#160;} <span class="comment">// namespace internal</span></div>
<div class="line"><a name="l00734"></a><span class="lineno">  734</span>&#160; </div>
<div class="line"><a name="l00735"></a><span class="lineno">  735</span>&#160;<span class="keyword">template</span>&lt;&gt; <span class="keyword">struct </span>NumTraits&lt;<a class="code" href="namespaceEigen.html">Eigen</a>::bfloat16&gt;</div>
<div class="line"><a name="l00736"></a><span class="lineno">  736</span>&#160;    : GenericNumTraits&lt;Eigen::bfloat16&gt;</div>
<div class="line"><a name="l00737"></a><span class="lineno">  737</span>&#160;{</div>
<div class="line"><a name="l00738"></a><span class="lineno">  738</span>&#160;  <span class="keyword">enum</span> {</div>
<div class="line"><a name="l00739"></a><span class="lineno">  739</span>&#160;    IsSigned = <span class="keyword">true</span>,</div>
<div class="line"><a name="l00740"></a><span class="lineno">  740</span>&#160;    IsInteger = <span class="keyword">false</span>,</div>
<div class="line"><a name="l00741"></a><span class="lineno">  741</span>&#160;    IsComplex = <span class="keyword">false</span>,</div>
<div class="line"><a name="l00742"></a><span class="lineno">  742</span>&#160;    RequireInitialization = <span class="keyword">false</span></div>
<div class="line"><a name="l00743"></a><span class="lineno">  743</span>&#160;  };</div>
<div class="line"><a name="l00744"></a><span class="lineno">  744</span>&#160; </div>
<div class="line"><a name="l00745"></a><span class="lineno">  745</span>&#160;  EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR <span class="keyword">static</span> EIGEN_STRONG_INLINE Eigen::bfloat16 epsilon() {</div>
<div class="line"><a name="l00746"></a><span class="lineno">  746</span>&#160;    <span class="keywordflow">return</span> bfloat16_impl::raw_uint16_to_bfloat16(0x3c00);</div>
<div class="line"><a name="l00747"></a><span class="lineno">  747</span>&#160;  }</div>
<div class="line"><a name="l00748"></a><span class="lineno">  748</span>&#160;  EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR <span class="keyword">static</span> EIGEN_STRONG_INLINE Eigen::bfloat16 dummy_precision() {</div>
<div class="line"><a name="l00749"></a><span class="lineno">  749</span>&#160;    <span class="keywordflow">return</span> bfloat16_impl::raw_uint16_to_bfloat16(0x3D4D);  <span class="comment">// bfloat16(5e-2f);</span></div>
<div class="line"><a name="l00750"></a><span class="lineno">  750</span>&#160;  }</div>
<div class="line"><a name="l00751"></a><span class="lineno">  751</span>&#160;  EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR <span class="keyword">static</span> EIGEN_STRONG_INLINE Eigen::bfloat16 highest() {</div>
<div class="line"><a name="l00752"></a><span class="lineno">  752</span>&#160;    <span class="keywordflow">return</span> bfloat16_impl::raw_uint16_to_bfloat16(0x7F7F);</div>
<div class="line"><a name="l00753"></a><span class="lineno">  753</span>&#160;  }</div>
<div class="line"><a name="l00754"></a><span class="lineno">  754</span>&#160;  EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR <span class="keyword">static</span> EIGEN_STRONG_INLINE Eigen::bfloat16 lowest() {</div>
<div class="line"><a name="l00755"></a><span class="lineno">  755</span>&#160;    <span class="keywordflow">return</span> bfloat16_impl::raw_uint16_to_bfloat16(0xFF7F);</div>
<div class="line"><a name="l00756"></a><span class="lineno">  756</span>&#160;  }</div>
<div class="line"><a name="l00757"></a><span class="lineno">  757</span>&#160;  EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR <span class="keyword">static</span> EIGEN_STRONG_INLINE Eigen::bfloat16 infinity() {</div>
<div class="line"><a name="l00758"></a><span class="lineno">  758</span>&#160;    <span class="keywordflow">return</span> bfloat16_impl::raw_uint16_to_bfloat16(0x7f80);</div>
<div class="line"><a name="l00759"></a><span class="lineno">  759</span>&#160;  }</div>
<div class="line"><a name="l00760"></a><span class="lineno">  760</span>&#160;  EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR <span class="keyword">static</span> EIGEN_STRONG_INLINE Eigen::bfloat16 quiet_NaN() {</div>
<div class="line"><a name="l00761"></a><span class="lineno">  761</span>&#160;    <span class="keywordflow">return</span> bfloat16_impl::raw_uint16_to_bfloat16(0x7fc0);</div>
<div class="line"><a name="l00762"></a><span class="lineno">  762</span>&#160;  }</div>
<div class="line"><a name="l00763"></a><span class="lineno">  763</span>&#160;};</div>
<div class="line"><a name="l00764"></a><span class="lineno">  764</span>&#160; </div>
<div class="line"><a name="l00765"></a><span class="lineno">  765</span>&#160;} <span class="comment">// namespace Eigen</span></div>
<div class="line"><a name="l00766"></a><span class="lineno">  766</span>&#160; </div>
<div class="line"><a name="l00767"></a><span class="lineno">  767</span>&#160; </div>
<div class="line"><a name="l00768"></a><span class="lineno">  768</span>&#160;<span class="preprocessor">#if defined(EIGEN_HAS_HIP_BF16)</span></div>
<div class="line"><a name="l00769"></a><span class="lineno">  769</span>&#160;<span class="preprocessor">  #pragma pop_macro(&quot;EIGEN_CONSTEXPR&quot;</span>)</div>
<div class="line"><a name="l00770"></a><span class="lineno">  770</span>&#160;<span class="preprocessor">#endif</span></div>
<div class="line"><a name="l00771"></a><span class="lineno">  771</span>&#160; </div>
<div class="line"><a name="l00772"></a><span class="lineno">  772</span>&#160;<span class="keyword">namespace </span><a class="code" href="namespaceEigen.html">Eigen</a> {</div>
<div class="line"><a name="l00773"></a><span class="lineno">  773</span>&#160;<span class="keyword">namespace </span>numext {</div>
<div class="line"><a name="l00774"></a><span class="lineno">  774</span>&#160; </div>
<div class="line"><a name="l00775"></a><span class="lineno">  775</span>&#160;<span class="keyword">template</span>&lt;&gt;</div>
<div class="line"><a name="l00776"></a><span class="lineno">  776</span>&#160;EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE</div>
<div class="line"><a name="l00777"></a><span class="lineno">  777</span>&#160;bool (<a class="code" href="namespaceEigen.html#a99adfc5178f3fd5488304284388b2a10">isnan</a>)(<span class="keyword">const</span> Eigen::bfloat16&amp; h) {</div>
<div class="line"><a name="l00778"></a><span class="lineno">  778</span>&#160;  <span class="keywordflow">return</span> (bfloat16_impl::isnan)(h);</div>
<div class="line"><a name="l00779"></a><span class="lineno">  779</span>&#160;}</div>
<div class="line"><a name="l00780"></a><span class="lineno">  780</span>&#160; </div>
<div class="line"><a name="l00781"></a><span class="lineno">  781</span>&#160;<span class="keyword">template</span>&lt;&gt;</div>
<div class="line"><a name="l00782"></a><span class="lineno">  782</span>&#160;EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE</div>
<div class="line"><a name="l00783"></a><span class="lineno">  783</span>&#160;bool (<a class="code" href="namespaceEigen.html#a1f1103712e337c4c96a05f949637a4c8">isinf</a>)(<span class="keyword">const</span> Eigen::bfloat16&amp; h) {</div>
<div class="line"><a name="l00784"></a><span class="lineno">  784</span>&#160;  <span class="keywordflow">return</span> (bfloat16_impl::isinf)(h);</div>
<div class="line"><a name="l00785"></a><span class="lineno">  785</span>&#160;}</div>
<div class="line"><a name="l00786"></a><span class="lineno">  786</span>&#160; </div>
<div class="line"><a name="l00787"></a><span class="lineno">  787</span>&#160;<span class="keyword">template</span>&lt;&gt;</div>
<div class="line"><a name="l00788"></a><span class="lineno">  788</span>&#160;EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE</div>
<div class="line"><a name="l00789"></a><span class="lineno">  789</span>&#160;bool (<a class="code" href="namespaceEigen.html#aba24ec81dec745a00b7f33adead89811">isfinite</a>)(<span class="keyword">const</span> Eigen::bfloat16&amp; h) {</div>
<div class="line"><a name="l00790"></a><span class="lineno">  790</span>&#160;  <span class="keywordflow">return</span> (bfloat16_impl::isfinite)(h);</div>
<div class="line"><a name="l00791"></a><span class="lineno">  791</span>&#160;}</div>
<div class="line"><a name="l00792"></a><span class="lineno">  792</span>&#160; </div>
<div class="line"><a name="l00793"></a><span class="lineno">  793</span>&#160;<span class="keyword">template</span> &lt;&gt;</div>
<div class="line"><a name="l00794"></a><span class="lineno">  794</span>&#160;EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC Eigen::bfloat16 bit_cast&lt;Eigen::bfloat16, uint16_t&gt;(<span class="keyword">const</span> uint16_t&amp; src) {</div>
<div class="line"><a name="l00795"></a><span class="lineno">  795</span>&#160;  <span class="keywordflow">return</span> Eigen::bfloat16_impl::raw_uint16_to_bfloat16(src);</div>
<div class="line"><a name="l00796"></a><span class="lineno">  796</span>&#160;}</div>
<div class="line"><a name="l00797"></a><span class="lineno">  797</span>&#160; </div>
<div class="line"><a name="l00798"></a><span class="lineno">  798</span>&#160;<span class="keyword">template</span> &lt;&gt;</div>
<div class="line"><a name="l00799"></a><span class="lineno">  799</span>&#160;EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC uint16_t bit_cast&lt;uint16_t, Eigen::bfloat16&gt;(<span class="keyword">const</span> Eigen::bfloat16&amp; src) {</div>
<div class="line"><a name="l00800"></a><span class="lineno">  800</span>&#160;  <span class="keywordflow">return</span> Eigen::bfloat16_impl::raw_bfloat16_as_uint16(src);</div>
<div class="line"><a name="l00801"></a><span class="lineno">  801</span>&#160;}</div>
<div class="line"><a name="l00802"></a><span class="lineno">  802</span>&#160; </div>
<div class="line"><a name="l00803"></a><span class="lineno">  803</span>&#160;}  <span class="comment">// namespace numext</span></div>
<div class="line"><a name="l00804"></a><span class="lineno">  804</span>&#160;}  <span class="comment">// namespace Eigen</span></div>
<div class="line"><a name="l00805"></a><span class="lineno">  805</span>&#160; </div>
<div class="line"><a name="l00806"></a><span class="lineno">  806</span>&#160;<span class="preprocessor">#if EIGEN_HAS_STD_HASH</span></div>
<div class="line"><a name="l00807"></a><span class="lineno">  807</span>&#160;<span class="keyword">namespace </span>std {</div>
<div class="line"><a name="l00808"></a><span class="lineno">  808</span>&#160;<span class="keyword">template</span> &lt;&gt;</div>
<div class="line"><a name="l00809"></a><span class="lineno">  809</span>&#160;<span class="keyword">struct </span>hash&lt;<a class="code" href="namespaceEigen.html">Eigen</a>::bfloat16&gt; {</div>
<div class="line"><a name="l00810"></a><span class="lineno">  810</span>&#160;  EIGEN_STRONG_INLINE std::size_t operator()(<span class="keyword">const</span> Eigen::bfloat16&amp; a)<span class="keyword"> const </span>{</div>
<div class="line"><a name="l00811"></a><span class="lineno">  811</span>&#160;    <span class="keywordflow">return</span> <span class="keyword">static_cast&lt;</span>std::size_t<span class="keyword">&gt;</span>(Eigen::numext::bit_cast&lt;Eigen::numext::uint16_t&gt;(a));</div>
<div class="line"><a name="l00812"></a><span class="lineno">  812</span>&#160;  }</div>
<div class="line"><a name="l00813"></a><span class="lineno">  813</span>&#160;};</div>
<div class="line"><a name="l00814"></a><span class="lineno">  814</span>&#160;} <span class="comment">// namespace std</span></div>
<div class="line"><a name="l00815"></a><span class="lineno">  815</span>&#160;<span class="preprocessor">#endif</span></div>
<div class="line"><a name="l00816"></a><span class="lineno">  816</span>&#160; </div>
<div class="line"><a name="l00817"></a><span class="lineno">  817</span>&#160;<span class="comment">// Add the missing shfl* intrinsics.</span></div>
<div class="line"><a name="l00818"></a><span class="lineno">  818</span>&#160;<span class="comment">// The __shfl* functions are only valid on HIP or _CUDA_ARCH_ &gt;= 300.</span></div>
<div class="line"><a name="l00819"></a><span class="lineno">  819</span>&#160;<span class="comment">//   CUDA defines them for (__CUDA_ARCH__ &gt;= 300 || !defined(__CUDA_ARCH__))</span></div>
<div class="line"><a name="l00820"></a><span class="lineno">  820</span>&#160;<span class="comment">//</span></div>
<div class="line"><a name="l00821"></a><span class="lineno">  821</span>&#160;<span class="comment">// HIP and CUDA prior to SDK 9.0 define</span></div>
<div class="line"><a name="l00822"></a><span class="lineno">  822</span>&#160;<span class="comment">//    __shfl, __shfl_up, __shfl_down, __shfl_xor for int and float</span></div>
<div class="line"><a name="l00823"></a><span class="lineno">  823</span>&#160;<span class="comment">// CUDA since 9.0 deprecates those and instead defines</span></div>
<div class="line"><a name="l00824"></a><span class="lineno">  824</span>&#160;<span class="comment">//    __shfl_sync, __shfl_up_sync, __shfl_down_sync, __shfl_xor_sync,</span></div>
<div class="line"><a name="l00825"></a><span class="lineno">  825</span>&#160;<span class="comment">//    with native support for __half and __nv_bfloat16</span></div>
<div class="line"><a name="l00826"></a><span class="lineno">  826</span>&#160;<span class="comment">//</span></div>
<div class="line"><a name="l00827"></a><span class="lineno">  827</span>&#160;<span class="comment">// Note that the following are __device__ - only functions.</span></div>
<div class="line"><a name="l00828"></a><span class="lineno">  828</span>&#160;<span class="preprocessor">#if defined(EIGEN_HIPCC)</span></div>
<div class="line"><a name="l00829"></a><span class="lineno">  829</span>&#160; </div>
<div class="line"><a name="l00830"></a><span class="lineno">  830</span>&#160;<span class="preprocessor">#if defined(EIGEN_HAS_HIP_BF16)</span></div>
<div class="line"><a name="l00831"></a><span class="lineno">  831</span>&#160; </div>
<div class="line"><a name="l00832"></a><span class="lineno">  832</span>&#160;__device__ EIGEN_STRONG_INLINE Eigen::bfloat16 __shfl(Eigen::bfloat16 var, <span class="keywordtype">int</span> srcLane, <span class="keywordtype">int</span> width=warpSize) {</div>
<div class="line"><a name="l00833"></a><span class="lineno">  833</span>&#160;  <span class="keyword">const</span> <span class="keywordtype">int</span> ivar = <span class="keyword">static_cast&lt;</span><span class="keywordtype">int</span><span class="keyword">&gt;</span>(Eigen::numext::bit_cast&lt;Eigen::numext::uint16_t&gt;(var));</div>
<div class="line"><a name="l00834"></a><span class="lineno">  834</span>&#160;  <span class="keywordflow">return</span> Eigen::numext::bit_cast&lt;Eigen::bfloat16&gt;(<span class="keyword">static_cast&lt;</span>Eigen::numext::uint16_t<span class="keyword">&gt;</span>(__shfl(ivar, srcLane, width)));</div>
<div class="line"><a name="l00835"></a><span class="lineno">  835</span>&#160;}</div>
<div class="line"><a name="l00836"></a><span class="lineno">  836</span>&#160; </div>
<div class="line"><a name="l00837"></a><span class="lineno">  837</span>&#160;__device__ EIGEN_STRONG_INLINE Eigen::bfloat16 __shfl_up(Eigen::bfloat16 var, <span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> delta, <span class="keywordtype">int</span> width=warpSize) {</div>
<div class="line"><a name="l00838"></a><span class="lineno">  838</span>&#160;  <span class="keyword">const</span> <span class="keywordtype">int</span> ivar = <span class="keyword">static_cast&lt;</span><span class="keywordtype">int</span><span class="keyword">&gt;</span>(Eigen::numext::bit_cast&lt;Eigen::numext::uint16_t&gt;(var));</div>
<div class="line"><a name="l00839"></a><span class="lineno">  839</span>&#160;  <span class="keywordflow">return</span> Eigen::numext::bit_cast&lt;Eigen::bfloat16&gt;(<span class="keyword">static_cast&lt;</span>Eigen::numext::uint16_t<span class="keyword">&gt;</span>(__shfl_up(ivar, delta, width)));</div>
<div class="line"><a name="l00840"></a><span class="lineno">  840</span>&#160;}</div>
<div class="line"><a name="l00841"></a><span class="lineno">  841</span>&#160; </div>
<div class="line"><a name="l00842"></a><span class="lineno">  842</span>&#160;__device__ EIGEN_STRONG_INLINE Eigen::bfloat16 __shfl_down(Eigen::bfloat16 var, <span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> delta, <span class="keywordtype">int</span> width=warpSize) {</div>
<div class="line"><a name="l00843"></a><span class="lineno">  843</span>&#160;  <span class="keyword">const</span> <span class="keywordtype">int</span> ivar = <span class="keyword">static_cast&lt;</span><span class="keywordtype">int</span><span class="keyword">&gt;</span>(Eigen::numext::bit_cast&lt;Eigen::numext::uint16_t&gt;(var));</div>
<div class="line"><a name="l00844"></a><span class="lineno">  844</span>&#160;  <span class="keywordflow">return</span> Eigen::numext::bit_cast&lt;Eigen::bfloat16&gt;(<span class="keyword">static_cast&lt;</span>Eigen::numext::uint16_t<span class="keyword">&gt;</span>(__shfl_down(ivar, delta, width)));</div>
<div class="line"><a name="l00845"></a><span class="lineno">  845</span>&#160;}</div>
<div class="line"><a name="l00846"></a><span class="lineno">  846</span>&#160; </div>
<div class="line"><a name="l00847"></a><span class="lineno">  847</span>&#160;__device__ EIGEN_STRONG_INLINE Eigen::bfloat16 __shfl_xor(Eigen::bfloat16 var, <span class="keywordtype">int</span> laneMask, <span class="keywordtype">int</span> width=warpSize) {</div>
<div class="line"><a name="l00848"></a><span class="lineno">  848</span>&#160;  <span class="keyword">const</span> <span class="keywordtype">int</span> ivar = <span class="keyword">static_cast&lt;</span><span class="keywordtype">int</span><span class="keyword">&gt;</span>(Eigen::numext::bit_cast&lt;Eigen::numext::uint16_t&gt;(var));</div>
<div class="line"><a name="l00849"></a><span class="lineno">  849</span>&#160;  <span class="keywordflow">return</span> Eigen::numext::bit_cast&lt;Eigen::bfloat16&gt;(<span class="keyword">static_cast&lt;</span>Eigen::numext::uint16_t<span class="keyword">&gt;</span>(__shfl_xor(ivar, laneMask, width)));</div>
<div class="line"><a name="l00850"></a><span class="lineno">  850</span>&#160;}</div>
<div class="line"><a name="l00851"></a><span class="lineno">  851</span>&#160; </div>
<div class="line"><a name="l00852"></a><span class="lineno">  852</span>&#160;<span class="preprocessor">#endif </span><span class="comment">// HIP</span></div>
<div class="line"><a name="l00853"></a><span class="lineno">  853</span>&#160; </div>
<div class="line"><a name="l00854"></a><span class="lineno">  854</span>&#160;<span class="preprocessor">#endif </span><span class="comment">// __shfl*</span></div>
<div class="line"><a name="l00855"></a><span class="lineno">  855</span>&#160; </div>
<div class="line"><a name="l00856"></a><span class="lineno">  856</span>&#160;<span class="preprocessor">#if defined(EIGEN_HIPCC)</span></div>
<div class="line"><a name="l00857"></a><span class="lineno">  857</span>&#160;EIGEN_STRONG_INLINE __device__ Eigen::bfloat16 __ldg(<span class="keyword">const</span> Eigen::bfloat16* ptr) {</div>
<div class="line"><a name="l00858"></a><span class="lineno">  858</span>&#160;  <span class="keywordflow">return</span> Eigen::bfloat16_impl::raw_uint16_to_bfloat16(__ldg(Eigen::numext::bit_cast&lt;const Eigen::numext::uint16_t*&gt;(ptr)));</div>
<div class="line"><a name="l00859"></a><span class="lineno">  859</span>&#160;}</div>
<div class="line"><a name="l00860"></a><span class="lineno">  860</span>&#160;<span class="preprocessor">#endif </span><span class="comment">// __ldg</span></div>
<div class="line"><a name="l00861"></a><span class="lineno">  861</span>&#160; </div>
<div class="line"><a name="l00862"></a><span class="lineno">  862</span>&#160;<span class="preprocessor">#endif </span><span class="comment">// EIGEN_BFLOAT16_H</span></div>
<div class="ttc" id="anamespaceEigen_html"><div class="ttname"><a href="namespaceEigen.html">Eigen</a></div><div class="ttdoc">Namespace containing all symbols from the Eigen library.</div><div class="ttdef"><b>Definition:</b> Core:139</div></div>
<div class="ttc" id="anamespaceEigen_html_a0110c233d357169fd58fdf5656992a98"><div class="ttname"><a href="namespaceEigen.html#a0110c233d357169fd58fdf5656992a98">Eigen::tanh</a></div><div class="ttdeci">const Eigen::CwiseUnaryOp&lt; Eigen::internal::scalar_tanh_op&lt; typename Derived::Scalar &gt;, const Derived &gt; tanh(const Eigen::ArrayBase&lt; Derived &gt; &amp;x)</div></div>
<div class="ttc" id="anamespaceEigen_html_a0211fe61b9e390dfd8ca213fe9c7fca3"><div class="ttname"><a href="namespaceEigen.html#a0211fe61b9e390dfd8ca213fe9c7fca3">Eigen::rint</a></div><div class="ttdeci">const Eigen::CwiseUnaryOp&lt; Eigen::internal::scalar_rint_op&lt; typename Derived::Scalar &gt;, const Derived &gt; rint(const Eigen::ArrayBase&lt; Derived &gt; &amp;x)</div></div>
<div class="ttc" id="anamespaceEigen_html_a1f1103712e337c4c96a05f949637a4c8"><div class="ttname"><a href="namespaceEigen.html#a1f1103712e337c4c96a05f949637a4c8">Eigen::isinf</a></div><div class="ttdeci">const Eigen::CwiseUnaryOp&lt; Eigen::internal::scalar_isinf_op&lt; typename Derived::Scalar &gt;, const Derived &gt; isinf(const Eigen::ArrayBase&lt; Derived &gt; &amp;x)</div></div>
<div class="ttc" id="anamespaceEigen_html_a230744e17147d12e8ef3f2fc3796f64f"><div class="ttname"><a href="namespaceEigen.html#a230744e17147d12e8ef3f2fc3796f64f">Eigen::atan</a></div><div class="ttdeci">const Eigen::CwiseUnaryOp&lt; Eigen::internal::scalar_atan_op&lt; typename Derived::Scalar &gt;, const Derived &gt; atan(const Eigen::ArrayBase&lt; Derived &gt; &amp;x)</div></div>
<div class="ttc" id="anamespaceEigen_html_a25256faeec3ffd0f3615a0e1e45dfb14"><div class="ttname"><a href="namespaceEigen.html#a25256faeec3ffd0f3615a0e1e45dfb14">Eigen::log10</a></div><div class="ttdeci">const Eigen::CwiseUnaryOp&lt; Eigen::internal::scalar_log10_op&lt; typename Derived::Scalar &gt;, const Derived &gt; log10(const Eigen::ArrayBase&lt; Derived &gt; &amp;x)</div></div>
<div class="ttc" id="anamespaceEigen_html_a34b99a26a2a1e7ff985a5ace16eedfcb"><div class="ttname"><a href="namespaceEigen.html#a34b99a26a2a1e7ff985a5ace16eedfcb">Eigen::cosh</a></div><div class="ttdeci">const Eigen::CwiseUnaryOp&lt; Eigen::internal::scalar_cosh_op&lt; typename Derived::Scalar &gt;, const Derived &gt; cosh(const Eigen::ArrayBase&lt; Derived &gt; &amp;x)</div></div>
<div class="ttc" id="anamespaceEigen_html_a3bc116a6243f38c22f851581aa7b521a"><div class="ttname"><a href="namespaceEigen.html#a3bc116a6243f38c22f851581aa7b521a">Eigen::tan</a></div><div class="ttdeci">const Eigen::CwiseUnaryOp&lt; Eigen::internal::scalar_tan_op&lt; typename Derived::Scalar &gt;, const Derived &gt; tan(const Eigen::ArrayBase&lt; Derived &gt; &amp;x)</div></div>
<div class="ttc" id="anamespaceEigen_html_a3fe3a136370fefae062591304c6a7ebd"><div class="ttname"><a href="namespaceEigen.html#a3fe3a136370fefae062591304c6a7ebd">Eigen::acos</a></div><div class="ttdeci">const Eigen::CwiseUnaryOp&lt; Eigen::internal::scalar_acos_op&lt; typename Derived::Scalar &gt;, const Derived &gt; acos(const Eigen::ArrayBase&lt; Derived &gt; &amp;x)</div></div>
<div class="ttc" id="anamespaceEigen_html_a45d37a9f1c784eb8ab61ed24f07f436f"><div class="ttname"><a href="namespaceEigen.html#a45d37a9f1c784eb8ab61ed24f07f436f">Eigen::atanh</a></div><div class="ttdeci">const Eigen::CwiseUnaryOp&lt; Eigen::internal::scalar_atanh_op&lt; typename Derived::Scalar &gt;, const Derived &gt; atanh(const Eigen::ArrayBase&lt; Derived &gt; &amp;x)</div></div>
<div class="ttc" id="anamespaceEigen_html_a62e77e0933482dafde8fe197d9a2cfde"><div class="ttname"><a href="namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Eigen::Index</a></div><div class="ttdeci">EIGEN_DEFAULT_DENSE_INDEX_TYPE Index</div><div class="ttdoc">The Index type as used for the API.</div><div class="ttdef"><b>Definition:</b> Meta.h:59</div></div>
<div class="ttc" id="anamespaceEigen_html_a6c5c246b877ac331495d21e7a5d51616"><div class="ttname"><a href="namespaceEigen.html#a6c5c246b877ac331495d21e7a5d51616">Eigen::asin</a></div><div class="ttdeci">const Eigen::CwiseUnaryOp&lt; Eigen::internal::scalar_asin_op&lt; typename Derived::Scalar &gt;, const Derived &gt; asin(const Eigen::ArrayBase&lt; Derived &gt; &amp;x)</div></div>
<div class="ttc" id="anamespaceEigen_html_a727dd851cc82a62574145bc5abdc7aed"><div class="ttname"><a href="namespaceEigen.html#a727dd851cc82a62574145bc5abdc7aed">Eigen::asinh</a></div><div class="ttdeci">const Eigen::CwiseUnaryOp&lt; Eigen::internal::scalar_asinh_op&lt; typename Derived::Scalar &gt;, const Derived &gt; asinh(const Eigen::ArrayBase&lt; Derived &gt; &amp;x)</div></div>
<div class="ttc" id="anamespaceEigen_html_a9723b3ff0f2c99fe1081e3eb14380d4c"><div class="ttname"><a href="namespaceEigen.html#a9723b3ff0f2c99fe1081e3eb14380d4c">Eigen::operator*</a></div><div class="ttdeci">const Product&lt; MatrixDerived, PermutationDerived, AliasFreeProduct &gt; operator*(const MatrixBase&lt; MatrixDerived &gt; &amp;matrix, const PermutationBase&lt; PermutationDerived &gt; &amp;permutation)</div><div class="ttdef"><b>Definition:</b> PermutationMatrix.h:517</div></div>
<div class="ttc" id="anamespaceEigen_html_a97676fabe9a7466cc2ccb6a2d0f83471"><div class="ttname"><a href="namespaceEigen.html#a97676fabe9a7466cc2ccb6a2d0f83471">Eigen::acosh</a></div><div class="ttdeci">const Eigen::CwiseUnaryOp&lt; Eigen::internal::scalar_acosh_op&lt; typename Derived::Scalar &gt;, const Derived &gt; acosh(const Eigen::ArrayBase&lt; Derived &gt; &amp;x)</div></div>
<div class="ttc" id="anamespaceEigen_html_a99adfc5178f3fd5488304284388b2a10"><div class="ttname"><a href="namespaceEigen.html#a99adfc5178f3fd5488304284388b2a10">Eigen::isnan</a></div><div class="ttdeci">const Eigen::CwiseUnaryOp&lt; Eigen::internal::scalar_isnan_op&lt; typename Derived::Scalar &gt;, const Derived &gt; isnan(const Eigen::ArrayBase&lt; Derived &gt; &amp;x)</div></div>
<div class="ttc" id="anamespaceEigen_html_aa73e38be0689a463ae14141b9cf89c35"><div class="ttname"><a href="namespaceEigen.html#aa73e38be0689a463ae14141b9cf89c35">Eigen::ceil</a></div><div class="ttdeci">const Eigen::CwiseUnaryOp&lt; Eigen::internal::scalar_ceil_op&lt; typename Derived::Scalar &gt;, const Derived &gt; ceil(const Eigen::ArrayBase&lt; Derived &gt; &amp;x)</div></div>
<div class="ttc" id="anamespaceEigen_html_aba24ec81dec745a00b7f33adead89811"><div class="ttname"><a href="namespaceEigen.html#aba24ec81dec745a00b7f33adead89811">Eigen::isfinite</a></div><div class="ttdeci">const Eigen::CwiseUnaryOp&lt; Eigen::internal::scalar_isfinite_op&lt; typename Derived::Scalar &gt;, const Derived &gt; isfinite(const Eigen::ArrayBase&lt; Derived &gt; &amp;x)</div></div>
<div class="ttc" id="anamespaceEigen_html_abf03d773a87830bc7fde51bcd94c89a0"><div class="ttname"><a href="namespaceEigen.html#abf03d773a87830bc7fde51bcd94c89a0">Eigen::floor</a></div><div class="ttdeci">const Eigen::CwiseUnaryOp&lt; Eigen::internal::scalar_floor_op&lt; typename Derived::Scalar &gt;, const Derived &gt; floor(const Eigen::ArrayBase&lt; Derived &gt; &amp;x)</div></div>
<div class="ttc" id="anamespaceEigen_html_ac5c8a2cded6b59628f2de04f24d2fff4"><div class="ttname"><a href="namespaceEigen.html#ac5c8a2cded6b59628f2de04f24d2fff4">Eigen::log1p</a></div><div class="ttdeci">const Eigen::CwiseUnaryOp&lt; Eigen::internal::scalar_log1p_op&lt; typename Derived::Scalar &gt;, const Derived &gt; log1p(const Eigen::ArrayBase&lt; Derived &gt; &amp;x)</div></div>
<div class="ttc" id="anamespaceEigen_html_ac74dc920119b1eba45e9218d9f402afc"><div class="ttname"><a href="namespaceEigen.html#ac74dc920119b1eba45e9218d9f402afc">Eigen::real</a></div><div class="ttdeci">const Eigen::CwiseUnaryOp&lt; Eigen::internal::scalar_real_op&lt; typename Derived::Scalar &gt;, const Derived &gt; real(const Eigen::ArrayBase&lt; Derived &gt; &amp;x)</div></div>
<div class="ttc" id="anamespaceEigen_html_ad01d50a42869218f1d54af13f71517a6"><div class="ttname"><a href="namespaceEigen.html#ad01d50a42869218f1d54af13f71517a6">Eigen::cos</a></div><div class="ttdeci">const Eigen::CwiseUnaryOp&lt; Eigen::internal::scalar_cos_op&lt; typename Derived::Scalar &gt;, const Derived &gt; cos(const Eigen::ArrayBase&lt; Derived &gt; &amp;x)</div></div>
<div class="ttc" id="anamespaceEigen_html_ad2d0241ffaaa3b0b04ec70b59ab066d4"><div class="ttname"><a href="namespaceEigen.html#ad2d0241ffaaa3b0b04ec70b59ab066d4">Eigen::log2</a></div><div class="ttdeci">const Eigen::CwiseUnaryOp&lt; Eigen::internal::scalar_log2_op&lt; typename Derived::Scalar &gt;, const Derived &gt; log2(const Eigen::ArrayBase&lt; Derived &gt; &amp;x)</div></div>
<div class="ttc" id="anamespaceEigen_html_ad9eaa98e8016ef17024a18a2f3e5bef3"><div class="ttname"><a href="namespaceEigen.html#ad9eaa98e8016ef17024a18a2f3e5bef3">Eigen::round</a></div><div class="ttdeci">const Eigen::CwiseUnaryOp&lt; Eigen::internal::scalar_round_op&lt; typename Derived::Scalar &gt;, const Derived &gt; round(const Eigen::ArrayBase&lt; Derived &gt; &amp;x)</div></div>
<div class="ttc" id="anamespaceEigen_html_ae27242789e7e62a8c42579b79be59b1a"><div class="ttname"><a href="namespaceEigen.html#ae27242789e7e62a8c42579b79be59b1a">Eigen::abs</a></div><div class="ttdeci">const Eigen::CwiseUnaryOp&lt; Eigen::internal::scalar_abs_op&lt; typename Derived::Scalar &gt;, const Derived &gt; abs(const Eigen::ArrayBase&lt; Derived &gt; &amp;x)</div></div>
<div class="ttc" id="anamespaceEigen_html_ae491aecf7dab66ac7e11008c5766694d"><div class="ttname"><a href="namespaceEigen.html#ae491aecf7dab66ac7e11008c5766694d">Eigen::exp</a></div><div class="ttdeci">const Eigen::CwiseUnaryOp&lt; Eigen::internal::scalar_exp_op&lt; typename Derived::Scalar &gt;, const Derived &gt; exp(const Eigen::ArrayBase&lt; Derived &gt; &amp;x)</div></div>
<div class="ttc" id="anamespaceEigen_html_ae6e8ad270ff41c088d7651567594f796"><div class="ttname"><a href="namespaceEigen.html#ae6e8ad270ff41c088d7651567594f796">Eigen::sin</a></div><div class="ttdeci">const Eigen::CwiseUnaryOp&lt; Eigen::internal::scalar_sin_op&lt; typename Derived::Scalar &gt;, const Derived &gt; sin(const Eigen::ArrayBase&lt; Derived &gt; &amp;x)</div></div>
<div class="ttc" id="anamespaceEigen_html_ae7cb2544e4e745bc0067fe793e3f2f81"><div class="ttname"><a href="namespaceEigen.html#ae7cb2544e4e745bc0067fe793e3f2f81">Eigen::expm1</a></div><div class="ttdeci">const Eigen::CwiseUnaryOp&lt; Eigen::internal::scalar_expm1_op&lt; typename Derived::Scalar &gt;, const Derived &gt; expm1(const Eigen::ArrayBase&lt; Derived &gt; &amp;x)</div></div>
<div class="ttc" id="anamespaceEigen_html_ae8bb75ba4f5f30a7571146dbfa653c6d"><div class="ttname"><a href="namespaceEigen.html#ae8bb75ba4f5f30a7571146dbfa653c6d">Eigen::log</a></div><div class="ttdeci">const Eigen::CwiseUnaryOp&lt; Eigen::internal::scalar_log_op&lt; typename Derived::Scalar &gt;, const Derived &gt; log(const Eigen::ArrayBase&lt; Derived &gt; &amp;x)</div></div>
<div class="ttc" id="anamespaceEigen_html_af284ce359b6efd4b594a9f8a1f5e5d96"><div class="ttname"><a href="namespaceEigen.html#af284ce359b6efd4b594a9f8a1f5e5d96">Eigen::sinh</a></div><div class="ttdeci">const Eigen::CwiseUnaryOp&lt; Eigen::internal::scalar_sinh_op&lt; typename Derived::Scalar &gt;, const Derived &gt; sinh(const Eigen::ArrayBase&lt; Derived &gt; &amp;x)</div></div>
<div class="ttc" id="anamespaceEigen_html_af4f536e8ea56702e63088efb3706d1f0"><div class="ttname"><a href="namespaceEigen.html#af4f536e8ea56702e63088efb3706d1f0">Eigen::sqrt</a></div><div class="ttdeci">const Eigen::CwiseUnaryOp&lt; Eigen::internal::scalar_sqrt_op&lt; typename Derived::Scalar &gt;, const Derived &gt; sqrt(const Eigen::ArrayBase&lt; Derived &gt; &amp;x)</div></div>
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